Why the udder is forbidden by the Sages, how to purge it of its milk (קריעה שתי וערב and טיחה בכותל), and its status in a mixture (Shulchan Aruch, Yoreh De'ah 90 — 4 se'ifim)
הַכָּחָל (פֵּרוּשׁ הַדַּד שֶׁל הַבְּהֵמָה) אָסוּר מִדִּבְרֵי סוֹפְרִים, שֶׁאֵין בָּשָׂר שֶׁנִּתְבַּשֵּׁל בַּחֲלֵב שְׁחוּטָה אָסוּר מִן הַתּוֹרָה. לְפִיכָךְ אִם קְרָעוֹ וּמֵרֵק הֶחָלָב שֶׁבּוֹ — מֻתָּר לִצְלוֹתוֹ וּלְאָכְלוֹ; וְאִם קְרָעוֹ שְׁתִי וָעֵרֶב וְטָחוֹ בַּכֹּתֶל עַד שֶׁלֹּא נִשְׁאַר בּוֹ לַחְלוּחִית חָלָב — מֻתָּר לְבַשְּׁלוֹ עִם הַבָּשָׂר.
The kachal — the udder (the «teat» of the animal) — is forbidden by decree of the Sages (מדברי סופרים), because meat that has cooked in the milk of a slaughtered animal (שחוטה) is not forbidden by the Torah. That is why: if one has slit the udder and extracted the milk from it (מירק החלב), it is permitted to roast it and eat it; and if one has slit it crosswise (קריעה שתי וערב) and pressed it against the wall (טיחה בכותל) to the point that no trace of milk moisture remains in it, it is permitted to cook it with meat.
Shulchan Aruch, Yoreh De'ah 90:1LEVEL 01
Hebrew text of the Mechaber with a fluent English translation. Why the udder is de-rabbanan, how to purge it (קריעה שתי וערב, טיחה בכותל), roasting / cooking / frying, the ביטול בששים and the minhag, key concepts and practical cases.
📖 StudyLEVEL 02
In-depth pilpul: the sugya of Chullin 109b-110a, the yesod of חלב שחוטה דרבנן, the machloket Rambam / Rashba on חתיכה נעשית נבילה and the צירוף of the כחל, the plugta Maharshal / Mechaber on בדיעבד, the sugya of כבוש כמבושל בחלב שחוטה (Taz / Pri Megadim), חקירות and נפקא מינות.
📖 StudyLEVEL 03
Comparative tables (roasting / cooking / frying / pâté), golden rules of purging, the ביטול בששים with כחל מן המנין, classic pitfalls (dried udder, knife, spit) and memorization of the 4 se'ifim.
📖 StudyLEVEL 04
The practical halacha according to the Mechaber, the Rama, the Shach, the Taz and the Pitchei Teshuva, then the Sephardic (Yalkut Yosef) and Ashkenazi streams of psak. Note: the Shulchan Aruch HaRav does not deal with this siman — this is a level of psak, not "Daat HaRav".
📖 StudyThe udder contains milk, and the meat of the udder has, in a sense, «cooked in milk». But this milk comes from a slaughtered animal (חלב שחוטה), whereas the Torah only forbids meat cooked in the milk of a living animal. That is why the kachal is forbidden only by the Sages (Shulchan Aruch YD 90:1). In practice, after the milk has been purged, the udder becomes permitted again. For practical halacha, consult your Rav.
The Mechaber distinguishes two levels: to roast it (צלי), it is enough to slit it crosswise (קריעה שתי וערב); to cook it with meat, one must in addition press it against the wall (טיחה בכותל) until no trace of milk moisture remains. The Rama (se'if 2) adds that slitting and incising it several times in both directions is even preferable to pressing. For practical halacha, consult your Rav.
The Mechaber (se'if 1) teaches that one then measures the mixture: there must be sixty times (ביטול בששים) the volume of the kachal — and the kachal itself counts in that volume (כחל מן המנין). If there is sixty, the rest is permitted and only the kachal is forbidden; if there is less, everything is forbidden. Many have the custom (minhag) not to cook the kachal at all, even on its own. For practical halacha — especially in a case of significant loss (הפסד מרובה) — consult your Rav.