Make the night before! Melt butter in a skillet over medium heat. Cook & stir the mushrooms until their liquid is almost evaporated and they're beginning to brown, about 10 minutes. Set aside.
Place bread cubes in a greased 9x13" baking dish. Spread 1/2 cup of cheese over the bread in a layer, and distribute the asparagus pieces, mushrooms, red pepper, and onion over the cheese. Optional: add crispy cooked bacon or sausage on top of the bread
Whisk together eggs, milk, salt, dry mustard, and black pepper in a bowl, and pour mixture over the bread & veggies. Fold gently. Cover and refrigerate at least 6 hours overnight.
The next day, preheat oven to 375°.
Remove the casserole from the refrigerator and let stand for 30 minutes. Spread 1/2 cup cheese in a layer over the casserole.
Bake in the preheated oven until a knife inserted near the edge comes out clean, 40 minutes. Let stand 8 minutes before cutting into squares.