Grease your slow cooker (6 qt. size). Place the broccoli florets, shredded carrots, onion and garlic into the bottom. Top with the cream cheese, seasonings and broth. Give it all a stir, place the lid on and set the heat to low. Cook for 4-6 hours, until the broccoli is tender.

Once the broccoli is tender, use an immersion blender to puree some of the soup, until it is mostly smooth, but still with some chunks. Whisk together the milk, cream and flour and stir it into the soup, along with the cheeses. Place the lid back on and set the heat to high. Let this cook another 30-45 minutes, or until the soup has thickened slightly, is fully heated through and the cheese has fully melted. Taste and add more seasonings if it needs it, then serve.