In a large pot, melt butter; sautee onions and garlic in butter until onions are translucent -- about 5 minutes. Add broth and sprouts; cover and simmer for about 15 minutes or until sprouts are very tender.
Add milk, half and half, salt, pepper, paprika, parsley, and cheese. Stir until heated through and cheese is melted.
Puree in blender/food processor (in batches, if necessary) and serve.