Cut carrots into small strips.
Break apart broccoli florets into small pieces.
Saute Onion in 1 tbsp of melted butter until transparent.
Make a roux using remainder of melted butter and flour. Cook about 5 minutes over medium heat.
Add in half and half stirring constantly.
Add in chicken stock and simmer for 20 minutes.
Add vegetables and cook for 25 minutes over low heat.
If you want a smooth soup, at this point puree in a blender and return to heat or use immersion blender.
Add cheese and nutmeg.
Add salt and pepper to taste.