Daf Yomi - Beitza 15 - Cooking on Yom Tov by Reb Jay

It is assur to cook on Yom Tov for Shabbos (although the
Gemara in Pesachim 46a mentions Rav Chisda who says M'ikor
hadin it is muttar, in any case everyone agrees that Mid'rabanan
it is assur). It is muttar, however, on Yom Tov to cook more
than will be needed and use the left over for Shabbos. The Tur
writes that even if the person cooking openly said the food will
be used for the next day, it is muttar, as cooking a large amount
improves the taste. The Rokeach, however, writes that this
would be assur, as Chazal only allowed adding extra food to a
pot, is if the ikar cavana is for that day (the only way improper
kavana would hurt in this case is if the person cooking spoke it
out, not if it was merely thought), while the Aruch Hashulchan
explains the Tur as saying that in this case, kavana does not
matter (or, the Tur could be learned as saying that Ho'eel
miklayea leahorchim is a fact, regardless of whether the guests
come or not, or what the owner's intention was). The Tur brings
down b'shem the Baal Haitur, that if the person adds food after
they have eaten, this is considered harama and is assur (harama
that is not obvious would be muttar according to the Tur, for
example, cooking more than is needed, however, open trickery
is assur). If an Eiruv Tavshilin made, this enables one to cook on
Yom Tov for Shabbos directly. The mishna Berura writes that
even according to those that say that Hachana D'Rabba is an
issur D'oraysa, cooking with an Eiruv Tavshilin is still muttar
due to Ho'eel miklayea leahorchim (although according to this
shita, the cooking must be finished while there is still time for
the orchim to eat, meaning there must be time left over before
shkiya; for this reason, the Magen Avraham recommends
making early Shabbos when Yom Tov comes into Shabbos).