Grease a 4- to 6-quart slow cooker with the butter. Add the onion, carrot, broccoli, garlic, chicken broth, heavy cream, sea salt, and black pepper. Cover and cook on
HIGH for 3 hours, until the vegetables are tender.
For a smoother soup, transfer half the soup to a blender and blend until smooth. Return the pureed soup to the slow cooker. Stir in the cheddar cheese, in small batches, to get a silky texture.
Serve topped with additional shredded cheese, bacon, and red pepper flakes.