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Roughly chop the broccoli florets and place them in the bottom of the crockpot. Add the chopped onion, shredded carrots, cream cheese, and minced garlic.
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In a large bowl, whisk the chicken broth with nutmeg, salt, pepper, and cornstarch until smooth. Pour the mixture over the vegetables in the crockpot and stir to combine.
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Cover and cook on HIGH for 2-3 hours (or on LOW for 6-7 hours), until the broccoli is tender. For a smoother texture, use an immersion blender to blend the soup, leaving some chunks if preferred.
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Reduce the heat to LOW, then add the milk and shredded cheddar cheese. Cook for an additional 30 minutes, or until the cheese has melted completely.
