Preheat the oven to 425 degrees F (220 degrees C). Lightly grease a 9x13-inch baking dish.

Combine ham, asparagus, onion, and bell pepper in the prepared baking dish. Beat eggs, milk, flour, Parmesan, tarragon, salt, and pepper together in a large bowl; pour over ham mixture.

Bake in the preheated oven until a knife inserted into the center comes out clean, about 20 minutes. Sprinkle top with Cheddar cheese; continue baking until cheese melted, 3 to 5 minutes. Let stand 5 to 10 minutes before serving.