Lamb shoulder is a tender, affordable cut of meat and also one of the most important meats of the Spanish cuisine. The combination of briny ingredients and slow-roasting technique make this a juicy, elegant holiday centerpiece.
In a food processor, pulse together the pitted olives, garlic, cured lemon slices, olive oil and herbs to form a rustic paste. Be careful not to overprocess; you want the paste to stay a bit coarse.
Preheat the oven to 325 degrees F. Open the lamb shoulder up on a cutting board and use a sharp knife to trim and score the flesh. Season the inside with salt. Rub the inside of the lamb with the seasoning paste. Carefully roll the lamb tightly and truss, or tie, with butcher's twine. Season the outside of the roast with salt and pepper. Place the roast on a wire rack set inside a deep roasting pan. Roast the shoulder in the preheated oven for 1 hour 25 minutes.
After 1 hour 25 minutes, remove the lamb from the oven and check the internal temperature of the roast with a metal probe thermometer the inside should read between 145 and 150 degrees F. If the temperature is lower, return the lamb to the oven and keep cooking until the desired internal temperature is reached.Once the lamb is cooked, set it aside in a warm place to let it rest for at least 15 minutes before slicing and serving. Carefully remove the butcher's twine. With a sharp knife, carve the shoulder into thin slices. Arrange on a serving platter, season with coarse sea salt if you like, and serve immediately.