Prep the Ingredients: Peel and cube the potatoes, dice the onion, and cube the Velveeta cheese.
Add to the Crockpot: In your slow cooker, combine the frozen broccoli florets, cubed potatoes, diced onion, minced garlic, and chicken broth. Add the unsalted butter, cream of chicken soup, and cream of mushroom soup. Stir everything together to mix well.
Cook on Low: Set the slow cooker to low heat and cook for 6-7 hours, or until the potatoes are tender and easily pierced with a fork.
Thicken the Soup: About 30 minutes before serving, whisk the all-purpose flour with a few tablespoons of water to make a slurry. Stir it into the soup to help thicken the consistency.
Add the Cheese: Add the cubed Velveeta cheese to the crockpot. Stir gently until the cheese has melted and is fully incorporated into the soup, creating a creamy, cheesy base.
Serve and Enjoy: Once the cheese has melted and the soup is well combined, ladle it into bowls. Serve hot with your favorite bread or crackers on the side for dipping.