In a large skillet cook the onion, scallion, and mushrooms in oil over moderately low heat, stirring, until onion is softened. Add bell peppers and salt and pepper to taste, and cook over moderate heat, stirring, for 10-15 minutes, or until all the liquid the mushrooms give off is evaporated and the peppers are tender.
Arrange half the bread cubes in a buttered large shallow (4.5 quart) baking dish, spread half the vegetable mixture over them, and sprinkle half the Cheddar and half the Parmesan over the vegetables. Arrange the remaining bread cubes over the cheeses, top with the remaining vegetables, and then top again with the remaining cheeses.
In a bowl whisk together the eggs, milk, mustard, Tabasco, salt and pepper to taste. Pour the egg mixture over the strata, and chill, covered, overnight.
Let the strata stand at room temperature for 15 minutes, then bake in the middle of a preheated 350F oven for 50 minutes to 1 hour, or until it is puffed and golden and cooked through.
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