In a large pot, melt butter over medium heat. Add onions and garlic, cooking until softened.
Stir in flour and cook for 1 minute, then slowly add chicken broth while stirring.
Add chopped broccoli and let simmer for 10 minutes until tender.
Reduce heat and stir in heavy cream, cheddar cheese, salt, pepper, and nutmeg.
Simmer until the cheese is melted and the soup is smooth and creamy.
Serve warm with crusty bread.