Take the lamb shoulder out of the fridge 1 hour before you are ready to work with it.
Preheat the oven to 450˚F.
In a food processor or blender, combine worcestershire sauce, apple cider vinegar, sugar, soy sauce, garlic, sun dried tomatoes, mint leaves, parsley, lemon juice, and hot water; pulse to make a chunky sauce. Set aside.
Place the lamb shoulder, fatty-side up, on a working surface, like a large cutting board. Using a sharp knife, make several slashes across the top and rub it with the olive oil; season with salt and pepper.
Coat the lamb with half of the prepared sauce. Keep the other half in the fridge until ready to serve the lamb.
Arrange the onion rings and smashed garlic on the base of a roasting pan.
Place the lamb shoulder over the top of the onions, fatty side up.
Pour 1 cup of water into the roasting pan and cover it with aluminum foil.
Put the pan in the oven and turn down the heat to 350˚F. Roast for 3 hours.
Remove the foil and increase the heat to 425˚F. Check to see if there’s any liquid in the pan; if not, add a cup of water.
Continue to roast for about 20 to 25 minutes or until browned on top, and the internal temperature of the lamb registers at 145˚F. Start checking internal temperature at around the 15-minute mark. When done, remove it from the oven.
Transfer the lamb to a cutting board and loosely cover it with foil; let it rest for 20 minutes.
Drizzle it with the reserved sauce and serve.