In a medium pan over medium-high heat, sauté onions and garlic in 1 tablespoon butter until softened.

In a large pot, cook remaining butter with flour to create a roux, 3-4 minutes. Once pasty and thick, add in half-and-half and chicken stock. Let simmer for 15-20 minutes.

Add onions, garlic, broccoli, and nutmeg to mixture and simmer for another 25-30 minutes, until thickened.

Stir in cheddar cheese until melted, taste and add salt and pepper to your liking.

Optional: Puree soup to smooth out chunks, or serve as is.