Preheat oven to 375°F; lightly grease a 2-quart (11-by-7-inch) baking dish.
Melt 3 Tbsp. butter in a small pan over medium-high heat. Add flour; stir until blended, about 2 minutes. Whisk in milk and broth. Cook, stirring, until mixture forms a thick, smooth sauce, about 10 minutes. Season with salt and pepper. Stir in 1/4 cup Parmesan.
Bring a large pot of salted water to a boil. Add ziti; cook until softened, about 5 minutes. Add vegetables and bring back to a boil. Cook until pasta is almost done, about 3 minutes longer. Drain and return to pot.
Pour sauce over pasta and vegetables; mix well. Spread evenly in baking dish. In a small dish, mix remaining Parmesan and bread crumbs. Melt remaining butter, stir into bread-crumb mixture and sprinkle over top of casserole. Bake until casserole is bubbly and top is golden brown, 20 to 25 minutes.