Arrange the meat attractively on a round platter, so that each slice can be easily picked up with chopsticks or a fondue fork. Arrange vegetables on a second platter.
Fill a hot pot or nabe pot 2/3 full of dashi set on a burner on the table. Each diner picks up a piece of meat from the serving platter and swishes it around in the simmering broth until the red meat becomes pink, or cooked to the degree desired. Diners may alternate between meat and vegetables. The tofu breaks easily, so be careful when adding it to the pot. Diners eat from the pot, dipping the food into the dipping sauces which are placed in individual cups at each person's place.
Combine the water and kelp in a large pot. Bring the water to a boil, removing the kelp just before water boils since it emits a strong odor. If the fleshiest part of the kelp is still tough, return it to the water for a few more minutes, along with a little cold water. (Soft kelp means sufficient flavor has been extracted.) Remove the kelp and bring stock to a full boil.
Add 1/4 cup cold water to bring the temperature down quickly and add the bonito flakes. Bring to a boil, and then immediately remove from the heat. (If bonito flakes boil too long, the stock becomes bitter.) Allow the flakes to settle to the bottom of the pan, then filter the stock through cheesecloth. Yield: About 2 quarts
Combine the dashi, soy sauce, and mirin in a saucepan and bring to a boil. Let boil for a few minutes to reduce by 1/3, then remove from heat and cool. Stir in vinegar to taste. Pour sauce into individual cups.
Toast the sesame seeds in a heavy pan until lightly browned. Transfer warm seeds to a mortar and grind to a paste, or whirl in a blender. Add the dashi, soy sauce, mirin, sugar and sake, and mix well, using a spatula to blend and smooth the sauce. Add cayenne to taste. Pour sauce into individual cups.