In a large pot, melt the butter over medium heat and add the diced onion. Sauté until the onion is translucent, about 5 minutes.

Add the minced garlic and cook for another minute.

Pour in the broth and bring to a simmer. Add the chopped broccoli and cook until tender, about 10-15 minutes.

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

Stir in the heavy cream and shredded cheddar cheese, mixing until the cheese is melted and the soup is creamy.

Season with salt and pepper to taste, and serve warm.