Where does the concept of food transfer come from?

Question

If I cook a cheese omelet in a skillet, then wash the skillet and cook a steak in the same skillet the steak is considered to have absorbed the dairy-ness of the cheese and is now consider not kosher. What is the basis for this concept? Is there any passage in the Written Torah that this is based on, or is it only based on a Talmudic passage? Does anyone know the history of this concept?

Answer 1

In Bamidbar 31:23, the Torah says in the context of the vessels B'nei Yisroel obtained from the war against Midyan, כל דבר אשר יבוא באש, תעבירו באש וטהר "Anything that was used in fire should be passed through fire and will then become pure" The Ramban there brings the Gemara from Avoda Zora (75b) that this reference to purification refers to Kashering vessels from forbidden foods they may have absorbed when these vessels were owned by the Midianites (Also see the Ran on this Gemara.)

Hence, anything absorbed into a pot remains there until it is pushed out in the manner it was absorbed. The dairy in your skillet remains so when meat goes in it, a status of a forbidden meat and milk mixture is created. The Rabbis decreed that even after the absorbed food becomes distasteful (נותן טעם לפגם), that the dairy remainder would still create a forbidden mixture with meat and the pot would be forbidden. The food, however, would be permitted after the fact.

Answer 2

A basic question.
See Numbers (31, 23):

‏כג כָּל-דָּבָר אֲשֶׁר-יָבֹא בָאֵשׁ, תַּעֲבִירוּ בָאֵשׁ וְטָהֵר--אַךְ, בְּמֵי נִדָּה יִתְחַטָּא; וְכֹל אֲשֶׁר לֹא-יָבֹא בָּאֵשׁ, תַּעֲבִירוּ בַמָּיִם.‏
‎ 23 every thing that may abide the fire, ye shall make to go through the fire, and it shall be clean; nevertheless it shall be purified with the water of sprinkling; and all that abideth not the fire ye shall make to go through the water.

Why not use immediately the dishes? Let's look the Yalkut Shim'oni on the verse:

‏ כל דבר אשר יבא באש וגו' - תניא: אחד נותן טעם לפגם ואחד נותן טעם לשבח אסור, דברי ר' מאיר. ר' שמעון אומר: לשבח אסור לפגם מותר. מה טעם דר' מאיר? יליף מגיעולי נכרים דנותן טעם לפגם הוא ואפילו הכי אסריה רחמנא, הכי נמי לא שנא. ואידך, קדרה בת יומא נמי אי אפשר דלא פגמה פורתא. ‏ The Tanayim understand that the problem with the dishes of Midyanim is that they can provide a taste from the last cooked foods. There is no doubt that that is not an optimal reproduction of the taste. But we consider (following R.Shim'on) that the degradation of the taste is minor after a short period (less than 24h) ‏ ור' שמעון מה טעם? דתניא: לא תאכלו כל נבלה לגר אשר בשעריך - כל הראויה לגר - קרויה נבלה, ושאינה ראויה לגר - אינה קרויה נבלה. ור' מאיר, ההוא למעוטי סרוחה מעיקרא. ור' שמעון, סרוחה מעיקרא לא צריך קרא, עפרא בעלמא הוא. הלוקח כלי תשמיש מן הנכרים, את שדרכו להטביל - יטביל, להגעיל - יגעיל, ללבן באוּר - ילבן. השפוד והאסכלא מלבנן באור, הסכין שפה והיא טהורה. ‏

I shall leave the details of this Topic (Tosfot AZ 67b, Raah in Bedek Habayt, Ran in Chidushin and Rif).
Meat and milk also leave taste after cooking into the pan. When Milk enter into fleishig pan, he gives Taam Rishon, (See ramban Chulin 111b) and the tastes of meat and of milk are both prohibited (Bassar Bechalav)
The Ban of Bassar Bechalav occurs through cooking. One of the verses is Exodus 23, 19

לֹא-תְבַשֵּׁל גְּדִי, בַּחֲלֵב אִמּוֹ
Thou shalt not seethe a kid in its mother's milk

The encounter between this 2 tastes may prohibit them.

Common questions: 1- we do not get any taste. 2- our dishes do not absorb. 3- detergents destroy the tastes.
Answer: not absolutely. There are professional tasters. Anyway for each question consult a rabbi because of the great multi-factoriality of the topic