Add broccoli, onion, garlic, carrots, cream cheese, salt, pepper, nutmeg, and vegetable broth to slow cooker. Stir to combine. Cook on low for 4 to 5 hours or high for 2 to 3 hours. When cooking is complete, mix together tablespoons of water and cornstarch in a saucepan, then mix in Greek yogurt and warm water. Place on the stovetop on low heat and mix in cheddar cheese until creamy and melted. Whisk into the slow cooker, then ladle and serve.