1. In a large pot, melt the butter over medium heat. Add the chopped onion and cook until translucent, about 5 minutes.
2. Add the minced garlic and cook for another minute.
3. Add the broccoli florets and chicken broth. Bring to a boil, then reduce heat and simmer until the broccoli is tender, about 10-15 minutes.
4. Use a blender to puree the soup until smooth. Return the soup to the pot.
5. Stir in the heavy cream and shredded cheddar cheese. Cook over low heat until the cheese is melted and the soup is heated through. Season with salt and pepper to taste.