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.