Preheat the oven to 350 degrees F. Butter a baking dish.
Bring a pot of water to a boil. Cook the macaroni according to the package instructions until still firm. Drain and set aside.
Meanwhile, melt the butter in a pot over medium heat. Add the celery, broccoli and onion and cook, stirring, until the vegetables soften, 4 to 5 minutes. Use a wooden spoon to mash some of the broccoli. Sprinkle on the flour and dry mustard and stir to coat the vegetables. Pour in the milk, broth and half-and-half and cook, stirring, to allow it to warm up.
Add the Cheddar, processed cheese, 1/2 cup of the Parmesan and some salt and pepper and stir to melt the cheese. Add the macaroni and stir. Taste and check for seasoning. Pour into the prepared baking dish. Combine the breadcrumbs and remaining 1/2 cup Parmesan in a small bowl and sprinkle over the dish. Bake until bubbly, about 25 minutes.