In a large skillet, saute the mushrooms, onions and green pepper in butter until tender; set aside. Place one slice of ham on each tortilla. Top each with about 1/4 cup mushroom mixture. Combine cheeses; set aside 1/4 cup. Sprinkle remaining cheese over tortillas.
Roll up tortillas. Place seam side down in a greased 11x7-in. baking dish. In a large bowl, beat the flour, eggs, milk, garlic powder, salt and hot pepper sauce until blended.
Pour over tortillas. Sprinkle with reserved cheese. Cover and refrigerate for at least 30 minutes.
Bake, uncovered, at 350° for 35-45 minutes or until set.