In a large skillet cook the onion, the scallion, and the mushrooms in the oil over moderately low heat, stirring, until the onion is softened. Add the bell peppers and salt and pepper to taste, and cook the mixture over moderate heat, stirring for 10 to 15 minutes, or until most of the liquid the mushrooms give off is evaporated and the peppers are tender.
Arrange the bread cubes in a buttered, large, shallow (41/2 quart) baking dish, spread the vegetable mixture over them, and sprinkle the cheddar and the Parmesan over the vegetables. In a bowl, whisk together the eggs, milk, mustard, tabasco and salt and pepper to taste. Pour egg mixture over the vegetables and bread, and chill covered overnight. Let stand at room temperature for 15 minutes and bake in the middle of an oven preheated to 350 degrees F for 30 minutes covered and 30 minutes uncovered, or until it is puffed and golden and cooked through. Let stand at least 10 minutes.