In a large pot, over medium high heat, cook onion in butter until tender
Add in garlic and saute for 1 minute
Sprinkle in flour and whisk until golden brown to make a roux.
Stir in broth, broccoli, carrots, nutmeg, and paprika
Bring to a boil, then reduce heat and simmer for about 15 minutes or until vegetables are tender but firm
Stir in half & half and cheese
Simmer for an additional 2 minutes or until cheese has melted
Season with salt & pepper to taste
Serve and enjoy!