Preheat oven to 425º F (220 degrees C).
Lightly grease a 9×13 inch baking dish.
Mix ham, onion, peppers, and asparagus in the prepared baking dish.
In a large bowl, beat together eggs, milk, flour, Parmesan, tarragon, salt, and pepper. Pour over ham mixture.
Bake 20 minutes in 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.