Chop broccoli into florets and add them to the crockpot along with onion, carrots, cream cheese, and garlic.
In a separate bowl, whisk chicken broth, nutmeg, salt, pepper, and cornstarch until smooth. Pour over the vegetables.
Cover and cook on HIGH for 2–3 hours or LOW for 6–7 hours, until broccoli is tender.
For a smoother soup, blend with an immersion blender to your preferred consistency.
Reduce heat to LOW, stir in milk and shredded cheddar, and cook for another 30 minutes until cheese is fully melted.
Taste and adjust seasonings before serving.