Pre-heat the oven to 350F/180C. Put the duck breasts in a small ovenproof pan on medium heat and fry skin side down for a few minutes to render the fat. Sprinkle with salt and pepper, turn over and brown the other side for 1 minute. Wipe any fat out of the pan, return the duck, place in the oven and bake for 20 minutes. Transfer to a chopping board and keep warm. The sauce: pour all the pan juices into a saucepan with the stock and lychee syrup. Boil until reduced to 1 1/2 cups - about 15 minutes. Pour into a fat strainer, then pour the defatted stock back into the saucepan and set aside. Pour the oil into a large frying pan on medium-high heat and fry the white parts of the spring onions and the pepper for 1 minute. Add water chestnuts, mangetout, ginger and green parts of the spring onions. Deglaze the pan with the defatted stock mixture then stir in 16 lychees and the soy sauce. Bring to a boil, remove from the heat, stir in the arrowroot slurry, return to the heat and boil until thickened, about 30 seconds. The bok choy: wash the stems carefully. Place the heads on a steamer tray, cover and steam for 3 minutes. Season lightly with salt and pepper. To serve: Remove and discard the heavy fat and skin from the duck, then cut each breast across the grain into 1/4" slices. Place a steamed bok choy head in the middle of each plate and fan out the leaves. Spoon the duck and sauce on to the leaves and serve the rice on the side.