Chop garlic cloves and large dice onion and carrots. Preheat a large pot over medium heat. Cook butter, chopped garlic, diced onion, and carrots for 5 minutes.
Add broccoli florets to the pot with chicken broth. Place the lid on the pot and cook for 10 minutes.
Uncover the pot and blend the soup with an immersion blender. Add heavy cream and shredded cheddar cheese to the soup. Stir the soup until the cheese is melted. Season the broccoli cheese soup with salt, pepper, and nutmeg.
Hollow out a large round sourdough bread to create a bowl. Warm up the bread by toasting it in a 350º oven for 5 minutes or microwaving it for 1 minute. Ladle the broccoli cheese soup into the bread bowl and sprinkle with extra shredded cheddar cheese. Serve warm.