Heat a large oven-safe skillet over medium heat. Add the sausage and cook for 5 to 6 minutes, breaking it into small pieces, until browned. Transfer it to a plate, leaving the drippings in the skillet.
Add the onion and cook for 3 minutes. Stir in the garlic and cook for 30 seconds, just until fragrant.
Add the potatoes, paprika, pepper, and salt. Stir to coat, then cook for 5 minutes so the edges begin to brown.
Pour in the broth and cream. Return the sausage to the skillet, stir, and bring the mixture to a gentle simmer.
Cover and simmer for 12 to 15 minutes, stirring once, until the potatoes are fork-tender and most of the liquid has reduced.
Heat the oven to 425°F. Sprinkle the cheddar over the skillet and bake uncovered for 8 to 10 minutes, until melted and bubbling at the edges.
Rest for 5 minutes. Finish with parsley if using, then serve hot.