Place tofu in an airtight container and freeze for 24 hours. Remove from container and thaw, at least 3 hours. Squeeze out excess moisture with your hands or place tofu on paper towels and lay a heavy cutting board on top.

Whisk 1/4 cup soy sauce, brown sugar, 1 tablespoon rice wine vinegar, and sherry together in a bowl to make the cooking sauce.

Whisk water, white sugar, 3 tablespoons soy sauce, hoisin sauce, oyster sauce, 1 tablespoon rice wine vinegar, and chile-garlic sauce together in a small saucepan over medium-low heat. Add 1/4 teaspoon cornstarch at a time and whisk until thickened, 3 to 5 minutes. Store special sauce in the refrigerator until ready to serve.

Chop tofu roughly into small pieces. Heat 1 teaspoon sesame oil in a large skillet over high heat. Add tofu when oil is hot; stir-fry until tofu is browned, about 5 minutes. Set tofu aside in a bowl.

Heat remaining sesame oil in the skillet over high heat. Saute onion and garlic until browned and any excess liquid is absorbed, about 2 minutes. Add mushrooms, water chestnuts, and bamboo shoots. Cook over medium-high heat until any excess liquid is absorbed, 2 to 3 minutes. Add cooking sauce to the skillet and stir. Add tofu to the skillet. Cook until sauce is thickened and all vegetables are tender, 2 to 3 minutes more. Remove from heat.

Place radicchio, bean sprouts, noodles, peanuts, carrot, and green onions in individual bowls. Place tofu mixture in a serving bowl. Arrange lettuce leaves on a large plate. Put special sauce in a serving bowl with a spoon. Assemble by placing 2 to 3 lettuce leaves on a plate, topping with tofu and garnishes, and drizzling the special sauce on top.