In a large pot combine water, salt, sugar, juniper berries, cloves, bay leaves and peppercorns. Bring to a boil to infuse flavours and dissolve dry ingredients, cool. Place lamb in a very large plastic container and cover with brine. Brine lamb in the refrigerator overnight.
Drain lamb and transfer to a deep oven tray. Discard brine. To lamb, add stock, wine, garlic, bay leaves and rosemary. Set the combination steam oven to hot air with steam at 130°C, 100% humidity. Cook on the lowest oven shelf for 4 hours, turning lamb over halfway through cooking.
After 3 hours, place Jerusalem artichokes or potatoes onto a perforated tray, sprinkle with salt and add to the top oven shelf with the lamb and cook for 30 minutes. Remove from the oven and allow to air dry on the bench top for 5 minutes. Continue cooking lamb for a further 30 minutes.
Meanwhile, prepare the herb sauce by combining parsley, mint, thyme, garlic, anchovy, Dijon mustard, oil, vinegar and sugar in a blender; process until chunky. Season with salt and pepper and transfer to a serving bowl. Refrigerate until required.
Preheat a separate oven to 230°C (210°C hot air). Pour extra vegetable oil into a deep enamel tray and heat in the oven for 15 minutes on the lowest shelf. Carefully add Jerusalem artichokes or potatoes to the oil, turning so they are well coated in fat. Cook for 30 minutes. Set the oven to a full surface grill with hot air at 220°C.
Remove the lamb from the combination steam oven and transfer it to the highest shelf possible with the artichokes or potatoes, on the second shelf from the top. Quickly turn the artichokes over then continue cooking for a further 30 minutes, or until the lamb is roasted and golden.
To serve, place the lamb on a serving plate with artichokes or potatoes, drizzle with juices and garnish with bay leaves, rosemary and thyme. Serve with herb sauce.
Hot air is Gaggenau's terminology for fan forced.