Preheat the broiler. Slice the croissants in half horizontally. Arrange croissant halves, cut sides up, in a single layer on an extra--arge baking sheet. Broil 4 to 5 inches from the heat for 1 to 2 minutes or until light brown. Set aside.
In a very large skillet, cook bacon over medium heat until crisp. Drain bacon on paper towels, reserving 1 tablespoon drippings in skillet. Crumble bacon; set aside.
Cook onion, sweet peppers, mushrooms, and basil in hot bacon drippings about 5 minutes or until vegetables are almost tender, stirring occasionally. Add spinach; stir until wilted and well coated. Transfer onion mixture to a colander set in sink; drain. Stir in bacon. Set aside.
In a greased 3-quart rectangular baking dish, arrange croissant bottoms, cut sides up, in a single layer, overlapping slightly. Sprinkle cheese over croissants. Spoon onion mixture over cheese; add croissant tops, cut sides down.
In a large bowl, beat eggs with a rotary beater; beat in milk, mustard and black pepper. Carefully pour egg mixture over strata; gently press down on croissants. Cover and chill in the refrigerator for 8 to 24 hours.
Uncover strata. Let stand at room temperature for 30 minutes. Bake, uncovered, in a 325 degree F oven for 50 to 55 minutes or until a knife inserted near the center comes out clean and strata puffs up, covering with foil the last 15 minutes of baking time to avoid overbrowning. Remove from oven. Let stand for 10 minutes before serving. Serve warm. Makes 10 to 12 servings.