Melt butter in a large pot over medium heat. Add onion and cook until softened, about 5 minutes.

Add garlic and cook for 1 minute more.

Add broccoli florets and chicken broth. Bring to a boil, then reduce heat and simmer for 15-20 minutes, or until broccoli is tender.

Carefully transfer soup to a blender (or use an immersion blender) and blend until smooth.

Return soup to the pot and stir in heavy cream and cheddar cheese. Heat gently until cheese is melted and soup is heated through. Do not boil.

Season with salt and pepper to taste. Serve immediately.