Prep the veggies: Chop the broccoli into small florets and grate the carrots. Dice the onion for even cooking.
Dump and go: In your slow cooker, add the broccoli, carrots, onion, chicken broth, garlic powder, paprika, salt, and pepper. Stir to combine.
Cook low and slow: Cover and cook on low for 4–6 hours, or high for 2–3 hours, until the broccoli is tender and the soup smells fragrant and cozy.
Make the cheese base: In a small saucepan, melt the butter over medium heat. Whisk in the flour to create a roux, then slowly add the milk. Stir until thickened and smooth.
Combine everything: Pour the milk mixture into the slow cooker, stirring well. Add the shredded cheddar cheese and heavy cream. Stir until the cheese melts completely and the soup turns creamy and thick.
Taste and adjust: Add more salt, pepper, or cheese as needed. For a smoother texture, blend part of the soup with an immersion blender.
Serve hot: Ladle into bowls and top with extra cheese, croutons, or a sprinkle of paprika for garnish.