Place potato in a large saucepan, cover with cold water and bring to the boil over high heat. Drain, then transfer to a shallow roasting pan. Add stock, garlic and lemon halves and juice. Drizzle over oil and season.
Pat chicken dry with paper towel. Tie legs together with kitchen string, season, then place on top of potato and bake, adding sage and butter to pan in last 10 minutes of cooking, for 1 hour or until chicken juices run clear when thickest part of thigh is pierced with a skewer. Serve with broccolini.
Tuck the wings under the chicken before roasting, to stop the wing tips from burning and help the breast cook evenly.