Melt butter in a large pot or Dutch oven over medium heat.

Add onion and cook until softened, about 5 minutes.

Add garlic and cook for 1 minute more.

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

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 and cheddar cheese. Cook until cheese is melted and soup is heated through.

Season with salt and pepper to taste.

Garnish with a slice of carrot, if desired, and serve hot.