Cut the tough ends off the asparagus and discard. Chop the remaining asparagus spears in 1-inch pieces. Boil 4 minutes, drain, and set aside.
In a 2-quart casserole dish sprayed with cooking spray, layer the bread slices, 1 c cheese, ham, asparagus, and onion. In a bowl, whisk together the eggs, mustard, salt, pepper, garlic, and milk. Pour over the casserole. Refrigerate overnight.
The next morning, heat the oven to 350F. While oven is heating, have the strata out of the fridge to start warming up. Cook the strata 45 minutes. Top with remaining 1 c cheese and bake 5-10 minutes more or until set. Serves 6.
My ham gave off quite a bit off juice as this cooked. Not a problem, I just tilted the dish, let the juice run to a corner, and used a balled up paper towel to sop it up.