Add the onion, carrot, potato, and garlic. Cook until softened and lightly fragrant, about 5–7 minutes.
Add the broccoli, beef broth, salt, and black pepper. Bring to a gentle simmer, then lower the heat and cook for 20–25 minutes, until all vegetables are tender.
Remove from heat and let the soup rest for 5 minutes.
Blend the soup using an immersion blender until smooth.
Stir in the heavy cream and shredded cheddar cheese. Adjust salt and black pepper as needed.
Add the nutmeg and simmer gently for 5 more minutes.