In a skillet, brown the sausage slices over medium heat until golden, then transfer to the crockpot.
Add diced potatoes, onion, garlic, and chicken broth into the crockpot. Stir gently to combine.
Cover and cook on low for 6-7 hours or on high for 3-4 hours until the potatoes are tender.
In a small saucepan, melt butter and whisk in flour to make a roux. Slowly add milk or cream while whisking until smooth and thickened.
Pour the mixture into the crockpot and stir well. Add shredded cheese and cook for another 15 minutes.
Season with salt and black pepper, then serve warm topped with chopped parsley.