Lightly grease a 11-inch deep pie plate with a pat of butter, OR you can also use a rectangular 2.15-quart baking dish.
Arrange the slices of bread on the bottom of the baking dish, allowing some edges to hang over the sides.
Layer the prosciutto over the bread slices.
Top with tomatoes and asparagus.
Sprinkle cheese over the asparagus and set aside.
In a large mixing bowl, combine the eggs and milk; whisk the two until well blended.
Season the mixture with salt, pepper and nutmeg; whisk until combined.
Pour the egg mixture into previously prepared dish; use your hands to push the ingredients down to soak up all the liquid. If liquid mixture does not seem enough for all the ingredients, in a separate bowl, mix one more egg with 1/2 cup milk and add to casserole.
Cover the casserole with foil and refrigerate it overnight.
Preheat the oven to 350°F.
While preheating oven, remove strata from fridge, uncover and let stand on counter for several minutes.
Bake the strata uncovered for 50 to 60 minutes, or until the eggs are cooked and the top is puffed and golden brown.
Remove from oven and let stand several minutes before serving.