In a large pot, melt some butter over medium heat. Add chopped onion and cook until translucent, about 5 minutes.

Add minced garlic and cook for another minute until fragrant.

Add broccoli florets and cook for a few minutes until slightly tender.

Pour in the broth, bring to a boil, then reduce heat and simmer for 20 minutes until broccoli is very tender.

Use an immersion blender to puree the soup until smooth, or transfer to a blender in batches.

Return the pureed soup to the heat, then stir in the cheddar cheese and heavy cream until melted and heated through.

Taste and adjust seasonings as needed. Serve hot garnished with extra cheese or fresh herbs if desired.