On what is Eruv Tavshilin made
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Question
On what should one make an Eruv Tavshilin?
Answer
If you do not intend to bake on the holiday, you need a significant cooked dish, typically eaten with bread, such as meat, fish, eggs, etc. (the custom is to use an egg which is eaten with bread nowadays), and its size should be at least an olive's worth. If you intend to bake, you also need bread the size of an olive, preferably the size of an egg, and ideally whole.
Source
The Gemara in Beitza, page 15: "Beit Shammai says: two dishes, and Beit Hillel says: one dish." In the Gemara, it is stated: "That which you bake, bake, and that which you cook, cook" — from here Rabbi Elazar said: "One does not bake except on what is baked, and one does not cook except on what is cooked." From here, the sages derived the Eruv Tavshilin from the Torah. Rabbeinu Tam in Sefer HaYashar wrote that although Beit Shammai holds that one needs one dish, the cooked does not permit baking, and the baked does not permit cooking. However, Rabbi Yosef disagrees with him because in the Jerusalem Talmud, Tractate Beitza, Chapter 2: "That which you bake, bake, and that which you cook, cook. Rabbi Elazar says: bake on what is baked and cook on what is cooked. Rabbi Yehoshua says: bake and cook on what is cooked. What is the reason of Rabbi Elazar? That which you bake, bake, and that which you cook, cook. What is the reason of Rabbi Yehoshua? That which you bake, and that which you cook, cook." And since Rabbi Elazar was from the school of Shammai, and the law is not like him, one dish is sufficient.
The Halacha ruled in Shulchan Aruch, Siman 527, that both a dish and bread are needed. The Mishnah Berurah there explains that if one does not intend to bake, a dish is sufficient, and bread is not needed.
See Azmera Leshimcha, issue 205.