Ketchup, a Western ingredient that has been adopted by the Japanese, helps form a sweet glaze on both the mushrooms and tofu.
Preheat the broiler. In a small bowl, combine the ketchup, soy sauce, sherry and sesame oil. In another small bowl, blend 1 tablespoon of the ketchup sauce with the lemon juice and reserve.
Arrange the mushroom caps on a cookie sheet, stemmed side down; brush with the vegetable oil and season with salt and pepper. Broil 6 inches from the heat for 4 minutes, rotating the pan if necessary, until browned. Turn the caps and broil for 3 minutes, or until lightly browned. Brush the caps with some ketchup sauce and broil for 30 seconds, or until crisp and deeply browned. Turn, brush again with sauce and broil for 30 seconds longer. Stack the caps and slice into 1/4-inch strips.
On the cookie sheet, brush the tofu on both sides with some of the ketchup sauce. Broil for 1 minute, or until deeply browned and crisp. While still on the sheet, gently cut into 1-inch cubes.
In a bowl, toss the mushrooms, scallion, tomato and sprouts with the lemon dressing; season with salt and pepper. Using a spatula, transfer the tofu to the salad, toss lightly and serve.