Melt butter in a large nonstick saucepan over med-high heat. Add onion and garlic; sauté 3 minutes or until tender.

Add broth and broccoli. Bring to a boil. Reduce heat to medium and cook 10 minutes.

Combine milk and flour (to avoid lumps add a little milk to the flour to make a paste first, then gradually add remaining milk), stirring with a whisk until well blended. Add milk mixture to broccoli mixture.

Cook 5 minutes or until slightly thick, stirring constantly. Stir in pepper.

Remove from heat; add cheese, stirring until cheese melts.

Place 1/3 of the soup in a blender or food processor and process until smooth. Return pureed soup mixture to pan. Or you can use a stick emulsion blender and blend until 1/3 of the mixture is blended, leaving remaining broccoli chunks.