Peel the potatoes and cut into approx. 1-1.5 cm cubes. Season lightly with salt, pepper and paprika. Place in a coated dish, add 4 sprigs of rosemary and place in the preheated oven at 200 ° C top / bottom heat for approx. 40-45 minutes.
Season the rack of lamb with salt and pepper and then fry on both sides for approx. 2 minutes until it has a nice color. Then place on a sprig of rosemary in an ovenproof dish and place in the oven with the potatoes for 15-20 minutes.
Boil the frying residues in the pan with 300ml stock, add the red wine, the balsamic vinegar and the 4 peeled and flattened garlic cloves with a large knife. While the meat and potatoes are still in the oven, let them reduce. If desired, thicken a little at the end. The sauce should be quite runny.
Cut open the rack of lamb and serve with the potatoes and sauce on preheated plates.