Vegetable Cheese Strata

4 tsp. olive oil
1 large onion, diced (about 2 cups)
3 cloves garlic, minced (about 1 Tbsp.)
8 ounces white mushrooms sliced (about 3 cups)
Cooking spray
1 whole-wheat baguette, cubed (about 5 cups)
8 large eggs
8 large egg whites
2 cups non-fat milk
1 Tbsp. Dijon mustard
10 ounces broccoli, steamed until tender but still firm, cooled and chopped, or 1 (10-ounce) package frozen broccoli, thawed and chopped
1 5 to 6 oz. package spinach (optional)
1/2 cup freshly grated Parmesan cheese
4 oz. shredded part-skim mozzarella cheese (1 cup)
1/2 cup thinly sliced sun-dried tomatoes (not oil-packed), soaked in hot water until soft, then drained
1 Tbsp. minced fresh thyme
1/2 tsp. salt
1/2 tesp. freshly ground pepper

Heat 2 tsp. oil in skillet. Add onions and cook until softened and beginning to brown, 3 to 5 minutes. Add garlic and cook for one minute. Transfer to bowl and let cool. Heat the remaining oil in same skillet and cook the mushrooms until they begin to brown, 5 to 7 minutes. Remove from heat and cool completely. Coat a large 9 x 13 baking dish with cooking spray. Arrange bread cubes over the bottom. In a large bowl, beat the whole eggs, egg whites, milk, and mustard together until well incorporated. Add all remaining ingredients and stir. Pour this mixture over the bread. Cover with plastic wrap and refrigerate overnight or at least 8 hours. Remove plastic and bake at 350 until top forms a light brown crust, about 1 hour.