This delightful dish is an innovative and economical way to serve a do-it-yourself-style appetizer or main-dish. It is usually presented in a special lacquered wood or china tray with the required number of compartments. It is just as effective served on a tray in small bowls or dishes. The pancakes can be made in advance and kept refrigerated until needed, and many of the fillings can also be prepared ahead of time for convenience.
Sift the flour into a mixing bowl and make a well in the center. Add the beaten egg, water, milk and seasonings and beat until smooth, then set aside for 20 minutes.
Drain the Chinese mushrooms, reserving the liquid. Discard the stems, then squeeze out as much water as possible from the caps and shred them very finely. Place in a small pan and simmer for 6 minutes with 2 tablespoons soy sauce, 2 teaspoons sugar and enough reserved water to just cover. Drain well.
Peel the carrot; cut lengthwise into thin strips, then into fine shreds. Cut the shreds into 1-inch lengths. Heat a small pan, add a very little vegetable oil and a few drops of sesame oil and stir-fry the carrot until softened but still uncolored. Add a little salt, pepper and soy sauce and remove from the heat. Rinse out the pan.
Peel and grate the radish and cook in the same way as the carrot, omitting the soy sauce. Trim the green onions, cut into short lengths and shred finely. Stir-fry briefly in vegetable oil until just softened.
Beat the egg whites until slightly frothy, adding a very small pinch of salt and pepper. Rub a small omelet pan or a well-seasoned wok with oil and pour in the egg. Tilt the pan so that the egg runs thinly over as wide an area as possible. Cook until firm but not colored on the underside, then flip over and cook the other side briefly. Repeat this with the egg yolks, taking care to cook them gently so they do not burn. Cut into narrow shreds, then cut crosswise into short lengths.
Very thinly shred the kim chee, squeezing to remove as much liquid as possible. Cut the beef into paper-thin slices (having it partially frozen makes this easier, then cut crosswise into very thin shreds. Heat a little vegetable oil and sesame oil together in a pan or wok and stir-fry the beef until it changes color, then splash in 1 tablespoon soy sauce, a sprinkle of salt, pepper and sugar and a little extra sesame oil.
Toast the sesame seeds in a dry pan over moderate heat until they turn golden and begin to pop. Remove, cool slightly and grind to a fairly fine powder.
Mix the sauce ingredients together and divide among several dishes. Rub the omelet pan or wok again with oil. Pour in a large spoonful of the batter and cook until the underside is golden and small bubbles appear on the surface. Flip over and cook the other side. Continue to cook pancakes over medium heat until batter is used up, stacking the pancakes under a cloth.
Serve the pancakes and fillings at room temperature on a tray with the dipping sauce.