Preheat oven to 425 degrees F (220 degrees C). Lightly grease a 9x13 inch baking dish.
Mix the ham, onion, red bell peppers, and asparagus in the prepared baking dish. In a large bowl, beat together the eggs, milk, flour, Parmesan, tarragon, salt, and pepper. Pour over the ham mixture.
Bake 20 minutes in the preheated oven, or until a knife inserted in the center comes out clean. Sprinkle with Cheddar cheese. Continue baking 3 to 5 minutes, or until cheese is melted. Let stand 5 to 10 minutes before serving.