Heat the butter in a large pot over medium heat. Add the onion, carrot, broccoli, and garlic and cook for about 5 minutes, until the vegetables soften. Stir in the flour and cook until it evenly coats all of the vegetables. Add the stock and beer, stirring vigorously to keep the flour from clumping. Simmer for a few minutes, then pour the mixture (working in batches, if need be) into a blender and puree until mostly smooth (a bit of texture can be nice here). You can also use a hand blender to puree the soup in the pot. Return the soup to the pot and bring to a simmer over low heat. Stir in the milk and cheese. After the cheese has fully melted into the soup, season with salt and pepper and a few good shakes of Tabasco. Serve each bowl of soup with a Parmesan crisp floating in the middle.