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Placing hot roast into cold gravy: It is forbidden to place a piece of hot meat which is Yad Soledes into cold [liquid] gravy.
The reason for this is: because since [the meat] does not actually mix into the gravy, it thus cooks the outer layer that surrounds [the gravy] prior to the gravy having a chance to overpower it and cool it down.
Placing garlic and oil on a hot roast: It is forbidden to spread oil and garlic on a [piece of] roast while it is still hot to the point of Yad Soledes, even if it had been roasted from before Shabbos, as nevertheless [this will cause] the oil and garlic to cook.
Regarding if the above laws apply even if the meat has been placed into a Keli Sheiyni or Shelishi-See Q&A.
Summary of hot solid foods:
According to the understanding of some opinions in the above stated Halachas, the Alter Rebbe rules that a solid piece of food which is Yad Soledes, even if placed into another pot/dish which was never on the fire is still considered a Keli Rishon and thus retains all the laws explained above in Halacha 9. See Q&A for a thorough discussion on this topic!
Q&A on a Davar Gush
What is the definition of a Davar Gush/ Solid food?
Any food which is not able to flow is considered a Davar Gush. Thus, rice and the like which are cooked and do not flow when poured out but rather simply fall are considered a Davar Gush.
Solids that contain liquid: Is a solid piece of food that is placed together with liquid into a second vessel still considered a Keli Rishon [according to the stringent opinions], such as for example, soup that has solid pieces which are poured into a bowl? All the food is considered a Keli Sheiyni being that the liquid gets cooled off by the walls of the second vessel which in turn then cools off the solid.
Is a Davar Gush always considered a Keli Rishon even when placed into another vessel?
This matter is disputed amongst Poskim. Some Poskim rule that any Davar Gush that is Yad Soledes retains the same laws as does a Keli Rishon [that one may not place any uncooked food on it] even if it has now been placed in its 10th vessel. This applies until the food reaches less than Yad Soledes. Others Poskim, however, rule that such foods receive the same laws as do liquidly foods of which the ruling is that it becomes less stringent in a Keli Sheiyni and is totally permitted in a Keli Shelishi.
When a Davar Gush is picked up with a fork from a Keli Rishon does it now have the status of a Keli Sheiyni according to the lenient opinion?
No. According to all it retains a Keli Rishon status until placed into an actual vessel, in which case according to the lenient opinions it has the status of a Keli Sheiyni. Thus, when placing a piece of Yad Soledes kugal onto a plate with pickles then even according to the lenient opinion above, if the kugel was removed from the Keli Rishon with a fork the Kugel is only considered a Keli Sheiyni, and one must thus beware that they do not touch each other.
If a Davar Gush was placed into soup that is in a Keli Sheiyni, does it receive a Keli Sheiyni status even according to the stringent opinion?
Yes, as the liquid which now surrounds the Davar Gush cools it off and gives it the status of a Keli Sheiyni according to all.
May one place ketchup and the like on a hot piece of toasted Challah?
Tzaruch Iyun if this poses an issue of Bishul after Afiya.
May one place butter or margarine on a Yad Soledes Davar Gush that has been placed in a Keli Shelishi even according to the stringent opinion?
Yes, [as it contains the same dynamics as ketchup being that they too are precooked.] However, when doing so one must beware not to transgress the Nolad prohibition. It thus may not be done if enough of an amount is being melted that it will flow off the food and be recognizable, as explained in Halacha 8.
May one place Challah or baked products on a Davar Gush:
Seemingly it is permitted to do so as without liquid the baked products cannot cook.
 Admur 318:20; See also Kuntrus Achron 253:11 that says we suspect for Shach by Davar Gush if no Rotev.
 Admur 318:31
 Shach Yorah Deah 105:8, Taz 94:14; Rashal Gid Hanashe 44; Shabbos Kehalacha Vol. 1 p 24
 Toras Hasham, brought in Soles Lamincha on Toras Chatas 23:7; Kaf Hachaim 94:72; Ketzos Hashulchan 124 footnote 15; Shabbos Kehalacha Vol. 1 p 24
 Shabbos Kehalacha Vol. 1 p. 88-91
 Magen Avraham 318:45 [although the Tzemach Tzedek explains that the Magen Avraham himself does not hold of this opinion as the final Halacha. Nevertheless the Peri Megadim seems to rule to be stringent in this Lechatchilah]; Admur 253 Kuntrus Acharon 11 “I did not record the words of the M”A as according to the Shach in Y.D. 94 a Davar Gush never becomes a Keli Sheiyni..”; Implication of Admur 318:20 and 31 regarding roast and does not differentiate between Keli Rishon and Sheiyni; M”B 318:45 and 65 and 118; Ketzos Hashulchan 124 footnote 15 and 39; Seeming conclusion of Igros Moshe; See Piskeiy Admur p. 180; So rule regarding Issur Vihter in Yoreh Deah: Shach Y.D. 94:30; 105:8 [Rules that a Davar Gush has the ability to absorb taste into other foods even when in a Keli Sheiyni]; Issur Viheter 36:7; Rashal Gid Hanashe 44; Taz 94:14 [regarding knife-Duchka Desakina]; Beis Lechem Yehuda 94:26; Halachas Pesuka 94:7; Chavas Daas 94:26; Beis Yitzchak 3:3; Toras Hasheam, brought in Soles Lamincha on Toras Chatas 23:7; Erech Hashulchan 94:14; Aruch Hashulchan 94:32 [unless great loss]; Chochmas Adam 60:12 [is lenient in case of great loss]; Kaf Hacahim Y.D. 94:72
 Rama Y.D. 94:7; Peri Megadim; Chovas Daas; Chasam Sofer; Aruch Hashulchan; Igros Moshe seems to be lenient from the letter of the law; Tzemach Tzedek Yoreh Deah 65, and so seems to be the opinion of Admur from the fact that in Halacha 31 he omit’s the novelty of the Magen Avraham which is that even in a Keli Sheiyni the roast may not have garlic placed on it, and Admur omit’s the Keli Sheiyni ruling.
 In accordance to Admur, however the M”B rules clearly that one is to initially be stringent unless it is a time of need.
 M”B 318:45; 65; 118; Ketzos Hashulchan 124 footnote 15 and 39; So rule regarding Issur Viheter: Aruch Hashulchan 94:32; Kaf Hachaim Y.D. 94:72; Hakashrus 10:91
 Rav SHZ”A, based on that one does not intend on doing so and it is anyways only a doubt if it has the status of a Keli Rishon.
 Shabbos Kehalacha Vol. 1 p. 92
 Shabbos Kehalacha Vol. 1 p. 92
 So rules the Ketzos Hashulchan 124 footnote 39, based on Admur in Kuntrus Achron in 253 and Peri Megadim. However, the Darkei Teshuvah rules stringently in this.
 The Igros Moshe allows this even in a Keli Sheiyni, however Rav Farkash only permits it in a Keli Shelishi and asks on Igros Moshe that ketchup is not a liquid. Vetzaruch Iyun as the Igros Moshe rules that it is a liquid. Furthermore, if viewed as a solid it is certainly permitted as it was previously cooked.
 Shabbos Kehalacha Vol. 1 p. 95
 This may be done according to all as ketchup is a precooked liquid which has cooled and thus it itself is disputed whether it contains a cooking prohibition in reheating. Thus, since a Davar gush also is disputed whether it cooks in a Keli Shelishi, therefore one may be lenient. So, rules Igros Moshe
 Shabbos Kehalacha Vol. 1 p. 96