Preheat oven to 350 degrees F (175 degrees C). Butter a 9x13-inch baking dish with 1 teaspoon butter.
Bring a large pot of salted water to a boil; cook asparagus until tender yet firm to the bite, 2 to 3 minutes. Remove asparagus from the pot, reserving the water.
Cook noodles in the reserved water from asparagus until tender yet firm to the bite, 6 to 8 minutes. Drain.
Whisk milk, egg, flour, and pepper together in a bowl; stir in 2 cups Italian cheese blend and 1/2 cup Parmesan cheese, ham, and asparagus. Add noodles and toss to coat; transfer to the prepared baking dish.
Mix bread crumbs and melted butter together in a bowl; add remaining Italian cheese blend and Parmesan cheese. Sprinkle bread crumb mixture over noodle mixture.
Bake in the preheated oven until bubbling and top is lightly browned, 35 minutes. Let stand for 10 minutes before serving.