Melt butter in a large pot over medium-high heat, and sauté onion until soft, about 3 minutes. Add additional butter and flour, whisking for 3-5 minutes to create a roux. Whisk while adding the half-and-half and chicken stock. Simmer for 20 minutes.
Stir in the broccoli florets and grated carrot. Add salt, pepper and nutmeg. Simmer over low heat for 30-35 minutes
Remove soup from heat and pulse with an immersion blender until smooth. Or, puree the soup in batches in a food processor until smooth, adding mixture back to the pot.
Return pot to low heat and stir in cheddar cheese. Simmer for 10 minutes, and serve.
1 servings