Toss the potatoes and carrots with 2 tablespoons of the oil and season well. Place in a large, shallow roasting tin and cook in a preheated oven, 220°C (425°F), Gas Mark 7, for 5 minutes.
Meanwhile, mix the remaining oil with the mustard and garlic and season to taste. Spread over the skin of the lamb, then scatter the rosemary and breadcrumbs on top and press lightly into place.
Arrange the lamb racks in the roasting tin and cook for 20 minutes until the vegetables are tender and the lamb is cooked to your liking, then remove the lamb and vegetables from the tin and keep warm.
Place the roasting tin over a gentle heat on the hob and add the balsamic vinegar, redcurrant jelly and stock. Allow to bubble for 2 minutes, then serve with the meat and vegetables.