1. Bring a large pot of salted water to a boil over high heat. Preheat oven to 350°F and lightly grease an 11-by-7-inch baking dish. In a large skillet over medium-high heat, cook sausage, stirring and breaking up meat, until no longer pink, about 3 minutes. Add butter and stir well. Sprinkle flour on top and stir for 1 to 2 minutes. Slowly pour in milk and cook, stirring constantly, until smooth and thickened, 3 to 4 minutes. Season sauce with salt and pepper.
2. Add ziti to boiling water and cook until tender, about 5 minutes, then add broccoli and cook for 3 minutes. Drain ziti and broccoli in a colander and transfer to baking dish. Stir in sausage mixture.
3. Sprinkle Parmesan on top and bake until golden brown and mixture is bubbling, about 25 minutes. Serve hot.