Preheat the oven to 190°C, gas mark 5. Mix the stem ginger, garlic and 1 tbsp oil to a paste. Score the skin of the lamb and rub with half the paste. Season.
Set a large frying pan with the remaining oil over a high heat. Brown the lamb all over for 2-3 minutes then transfer to a baking tray. Roast for 30 minutes, or until done to your liking. Remove from the tray, cover with foil and leave to rest.
Meanwhile, drain any excess fat from the frying pan and return to a high heat. Cook the plums cut-side down for 3-5 minutes. Turn over, add the ginger syrup, soy sauce, cinnamon and remaining ginger paste. Cook for 5 minutes, until the plums are soft.
Carve the lamb into chops and serve with the sticky plums, rice and greens.