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

Add the minced garlic and sauté for another minute.

Add the broccoli florets and vegetable broth to the pot. Bring to a boil, then reduce heat and let simmer for about 15 minutes, until the broccoli is tender.

Stir in the heavy cream and bring the mixture back to a gentle simmer.

Using an immersion blender, blend the soup until smooth. Alternatively, carefully transfer it to a blender in batches.

Return the soup to the pot and stir in the shredded cheddar cheese until melted and smooth. Season with salt and pepper to taste.

Serve hot with toasted crusty bread.