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

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

Return the soup to the pot and stir in heavy cream, cheddar cheese, salt, and pepper. Heat through, but do not boil.

Serve immediately.