To a large slow cooker, add the broccoli, carrots, onion, butter, garlic, and salt and pepper.
To a small bowl, add in 1 cup of the broth and the cornstarch and whisk together well so the broth isn’t clumpy. Add this cornstarch slurry into the slow cooker with the remaining broth. Cook on LOW for 6-7 hours.
Once cooked, add in cheese and heavy cream, stir well, put the lid on top, and cook on HIGH for 30-40 minutes until the cheese is melted and everything is warmed through. Serve and enjoy!