Bishul/cooking is food prepared by heating in liquid. Why then is making tea/coffee not considered cooking?
The Daily Halacha Preparing Instant Coffee, Hot Chocolate and Tea on Shabbat explains the reasoning behind the discussion. There are two questions involved.
Instant coffee has already been cooked so that pouring hot water on it, is not considered bishul.
Tea leaves, would be cooked by putting them into hot water in a kli sheini, so that one may not put a tea bag into a cup and pour hot water on it from a kli rishon or put the tea bag into hot water in a kli sheni. See the details from the citation below.
Is it permissible to prepare instant coffee, hot chocolate or tea on Shabbat, by pouring hot water on the powder or tea leaves?
A Halachic principle establishes that when hot water is poured onto raw food from a “Keli Rishon,” meaning, from the original utensil in which it had been heated, it cooks the first layer of the food. Accordingly, it is forbidden to pour water directly from an urn or hot water kettle onto raw food. Seemingly, then, it should be forbidden to pour hot water directly from an urn or kettle onto instant coffee or hot chocolate powder.
However, there is another Halachic principle which states that one does not violate the Shabbat prohibition of cooking by cooking a food that had already been cooked previously. If a food had already been cooked, cooking it a second time does not constitute “cooking” as defined by Halacha. Therefore, it is permissible to pour hot water directly over instant coffee or chocolate powder. All powders made for instant cooking had already been cooked as part of their processing. Whether it’s hot chocolate powder, milk powder or baby formula, the processing of the powder entails cooking. Likewise, instant coffee has already undergone a process of roasting, and cooking a food that had been roasted does not violate the Shabbat prohibition of cooking. Therefore, it is permissible to pour hot water directly from an urn or kettle onto any instant powder or instant coffee on Shabbat.
This Halacha does not, however, apply to preparing tea from teabags. The leaves inside the bags are raw, and had not been previously cooked. As such, it is forbidden to pour hot water directly from an urn or kettle onto a teabag. One who wishes to prepare tea on Shabbat must first pour the hot water from the urn or kettle into an empty utensil, and then pour the water from that utensil into the teacup. Tea leaves are classified as “Kaleh Habishul” – a food that is easily cooked - and therefore one may not place them in the “Keli Sheni,” meaning, in a utensil into which water had been poured from an urn. Instead, one should pour the water from that utensil into the teacup. He may place the tea leaves into the teacup and pour the water onto the leaves from the “Keli Sheni,” or he can pour the water into the teacup and then place the tea leaves in the water in the teacup.
Summary: It is permissible to prepare instant coffee, hot chocolate and other powders by pouring hot water on the powder directly from the urn or kettle. To prepare tea, one must pour the water from the urn or kettle into a utensil, and then transfer the hot water from that utensil into the teacup.
As hot water is transferred from one utensil into another, it is considered as having lessened the strength of the hot water. Pouring from one vessel into another is considered less than the first vessel, but more than the second vessel. This means that the cooking of the tea leaves in the bag is permitted using irui kli sheni and therefore permitted by placing the tea leaves directly into a kli shlishi.
Although the aforementioned Mishna permits placing spices in a Kli Sheni containing hot water, the Mishna that appears on Shabbat 145b indicates that one may not place uncooked salted fish in a Kli Sheni filled with hot water. Similarly, one opinion recorded on Shabbat 42b asserts that salt is unlike spices and cooks even in a Kli Sheni. This opinion believes that since salt is easily cooked (Kalei Habishul), it can be cooked even in a Kli Sheni. The Sefer Yereim (102) believes that since we are not sure which items are similar to salt and can be cooked in a Kli Sheni, we must be concerned that virtually any item may fall into the category of Kalei Habishul. Thus, he urges that virtually no food be placed in a Kli Sheni containing hot water. The Tur (O.C. 318), however, challenges the Yereim's expansion of the concern for Kalei Habishul beyond the cases specifically mentioned by the Mishna and Gemara. Moreover, the concern expressed by the Yereim is not even alluded to by any of the great Rishonim such as the Rif, the Rambam, and the Rosh.
The Rama (318:5) cites the opinions of both the Yereim and the Tur. He notes, however, that common practice is not to place Challah even in a Kli Sheni due to concern that Challah is classified as Kalei Habishul. Parenthetically, we should explain that although the Challah was baked, people were concerned for the opinion of the Yereim that although we believe Ein Bishul Achar Bishul, cooking may occur after baking.
The Mishna Berura (318:42), citing the Magen Avraham, writes that the stringent practice applies to all items in accordance with the view of the Sefer Yereim. Thus, we must be concerned that almost all food items are Kalei Habishul. The Chazon Ish (O.C. 52:19), however, questions the expansion of the concern of Kalei Habishul beyond bread, which is specifically mentioned by the Rama. He suggests that perhaps bread is more easily cooked than other items since it was already baked. The Chazon Ish, nonetheless, honors the common practice to follow the stringent views of the Magen Avraham and Mishna Berura.
Is Tea Classified as Kalei Habishul?
The Yereim's concern applies only to items that the Mishna or Gemara does not specifically mention. The Mishna, however, specifically states that spices cannot be cooked in a Kli Sheni. Accordingly, why do the Mishna Berura and Aruch Hashulchan reject Rav Chaim's ruling that tea is a spice and we are permitted to prepare it in a Kli Sheni? Rav Shlomo Zalman Auerbach (cited in Shmeirat Shabbat Kehilchata 1: note 152) explains that the spices in the Mishna were large and unprocessed. Today, commercially available spices are ground very finely and present a concern for Kalei Habishul. Thus, one might argue that since tea leaves are incomparable to the Mishna's unprocessed spices, they should be classified as Kalei Habishul. Indeed, the Aruch Hashulchan notes that it is observable that tea cooks in a Kli Sheni.
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