In a large pot, melt the butter over medium heat. Add the minced garlic and sauté for a few minutes until fragrant.
Pour in the heavy cream and bring to a simmer.
Add the vegetable or chicken broth and bring to a simmer.
Add the chopped broccoli, potato and grated carrot to the pot. Cook for about 25-30 minutes, or until the broccoli is tender.
Stir in the shredded cheddar cheese until melted and well combined.
Season with salt and pepper to taste.
Serve hot, garnished with extra shredded cheese if desired. Enjoy your delicious broccoli cheddar soup!