Heat the oil in a 9-inch nonstick ovenproof skillet. Add the ham and cook over moderately high heat until lightly browned, about 1 minute. Add the mushrooms and cook until softened, about 2 minutes. Add 1 tablespoon of the soy sauce and simmer for 30 seconds. Add the snow peas and cook, stirring, for 30 seconds, then add the bean sprouts and cook, stirring, for 30 seconds. Season with salt and pepper. Push the shrimp into the vegetables and add the eggs, spreading them evenly. Bake the omelet in the oven for about 12 minutes, or until set in the center.