Chop carrots and celery. Place in a pot of water and boil for ten minutes. Drain the water, and then puree in a food processor or blender.
Cook the pasta according to package directions. Drain and return to the pot.
Chop the onion and garlic.
In a large saucepan, melt the better. Add chopped onion and garlic. Add black beans. Whisk in the flour. Slowly mix in the milk and simmer till thick. Season with salt, pepper, and old bay seasoning. Add the cheese, and stir to melt.
Combine the pureed veggies, the pasta, the veggie-bean-cheese mixture into the large saucepan. Transfer to a casserole dish. Top with parmesan cheese (1 ounce is about 1/4 cup). Broil in the oven on high for about 5 minutes.