Add the potatoes, broccoli, carrots, onion, garlic, and broth to your slow cooker. Stir gently to combine.

Cover and cook on LOW for 6–7 hours or HIGH for 3–4 hours, until the vegetables are tender and easily pierced with a fork.

In a small saucepan, melt butter over medium heat. Stir in flour and cook for 1–2 minutes until lightly golden. Slowly whisk in the cream, stirring constantly to avoid lumps. Once thickened, pour the mixture into the slow cooker and stir well.

Stir in the shredded cheddar cheese a handful at a time, mixing until melted and fully incorporated.

For a smoother soup, use an immersion blender to partially blend the mixture right in the slow cooker — or transfer half to a blender, then return it to the pot. Leave some chunks for texture if you prefer a rustic feel.

Taste and adjust seasoning with salt, pepper, and a pinch of paprika or cayenne for a gentle heat. Garnish with parsley and an extra sprinkle of cheddar before serving.