Heat butter in a soup pot over medium-high heat. Add onions and carrots; sauté for about 5 minutes. Add in garlic and stir for 30 seconds.
Add in broccoli, broth, paprika, cayenne, salt, pepper, and nutmeg. Stir well. Bring to a boil and reduce heat to a simmer.
Simmer, stirring occasionally, for 15 minutes until vegetables are completely softened. Stir in milk, and cook for 2 minutes. Remove from heat and use an immersion blender to blend soup to desired consistency. {You can use a regular blender but be careful when blending hot soup}
Add in cheese and stir until cheese melts. Serve and enjoy!
Notes
*You can use frozen cut broccoli or about 5 cups chopped fresh broccoli.