Melt butter in a 4-qt. saucepan over medium-high. Cook shallots, carrot, and onion until soft, 4–6 minutes. Stir in flour and cook for 2 minutes more. Add stock, milk, caraway seeds, salt, and pepper and simmer until soup is thickened, 8–10 minutes. Add cheddar and beer and cook until cheese is melted, 2–3 minutes. Ladle soup into bowls and top with Gorgonzola. Serve with crusty bread.