|In a medium saute pan melt the butter over medium heat and add the asparagus, shallots, and mushrooms. Allow the vegetables to saute for about 5 minutes, or until the mushrooms and shallots are softened and the asparagus can be easily speared with a fork.Meanwhile, mix the cheeses in a bowl with the salt and pepper and set aside. Then whisk together the eggs and milk and set aside.
Generously butter a 13 x 9 baking dish and layer everything as follows: one third of the bread cubes, followed by one third of the cooked vegetable mixture, followed by one-third of the cheese mixture. Repeat this layering two more times. Then, pour the egg and milk mixture over the entire dish, pushing down on the bread so it begins to soak up the custard. Cover the dish and chill it in the refrigerator for 6 hours, or up to 24.
Preheat the oven to 350 degrees F. Bring the strata to room temperature, then bake it for 40 to 45 minutes, or until it is puffed up the the bread tops are golden brown. Allow to cool slightly and serve warm.