In a large pot, sautee butter, onions and carrots 5-7 minutes.
Add garlic and flour. Cook for about 2 minutes, stirring so mixture won't burn.
Add broth, and broccoli. Cook over high until broccoli is tender. About 10 minutes.
Use an immersion blender and puree mixture just until large chunks are broken up.
Whisk in milk and bring back up to a simmer.
Add salt, pepper and nutmeg.
Slowly mix in cheese. Stir until melted.
Shred you own cheese instead of purchasing pre-shredded. Pre-shredded cheese can have an additive so the cheese won't clump together. This additive can prohibit the melting of the cheese. I used 2% milk. Can also use half-n-half