Preheat oven to 325°F (163°C). Flip lamb racks bone-side up and remove the membrane using a sharp knife and paper towels, then pat ribs dry.

In a small bowl, combine kosher salt, black pepper, garlic powder, dried oregano, dried rosemary, paprika, and ground cumin to make the dry rub.

Rub 2 tablespoons of olive oil onto both sides of the ribs, then sprinkle the dry rub mixture evenly and massage it into the meat.

Heat remaining 2 tablespoons of olive oil in the roasting pan over medium-high heat, sear ribs bone-side down for 3–4 minutes per side until golden, then arrange meat-side up.

In a small bowl, whisk together minced garlic, Dijon mustard, honey, and balsamic vinegar to form the mop sauce.

Pour beef or lamb stock into the pan around the ribs, add fresh rosemary sprigs and lemon halves to the liquid without submerging the meat.

Cover pan tightly with foil and roast in the preheated oven for 90 minutes without opening.

Remove foil, brush ribs with mop sauce, then roast uncovered for 45 minutes, basting with mop sauce every 15 minutes.

Brush ribs one final time with remaining mop sauce and roast uncovered for another 45 minutes until caramelized and meat thermometer reads 190–200°F.

Remove ribs from oven and let rest for 10 minutes. Pour pan drippings into a small bowl and serve alongside ribs.