Attach 4-5 rosemary sprigs to a wooden spoon handle with twine or rubber band to form a baster brush.
Bring the steaks to room temperature and season liberally with salt and pepper. Prepare the grill or charcoals or wood coals to high heat. Bank your coals to one side to intensify the heat. Or, heat a large, cast iron skillet over high heat and pre-heat the oven to 325°F.
In a small saucepot, warm about 1/2 cup olive oil with the garlic and a few small pieces of rosemary to infuse the oil (if your saucepot is grill-safe, you may warm it right on the grill).
Combine the parsley, rosemary, garlic, lemon zest and juice, anchovies, Worcestershire sauce, salt, pepper and olive oil in a food processor or blender and puree into sauce.
Place the potatoes in pot, cover with water and bring to a boil. Salt the water and cook to tender. Drain the potatoes and add back to the hot pot; add the stock and lemon juice or vinegar, olive oil, salt and pepper. Cover the pot to keep warm until you carve the steaks. Just before serving, add the chopped celery, onion and parsley; toss and serve.
Grill the steaks for 12-14 minutes, 6-7 minutes per side, turning once and basting frequently with the rosemary oil, to an internal temp of 125°F. If using a skillet, brown the steaks for 4 minutes on each side, then place in the oven and finish cooking, 6-8 minutes more. Remove the meat to a carving board and let rest, 10 minutes.
Grill the lemons dressed with olive oil, salt and pepper, cut side down, on the grill or in the skillet, 4-5 minutes.
Carve the fillet and sirloin off the bone and slice 1/2-inch thick, cutting perpendicular to the bone across the sirloin grain of the meat. Douse the meat with the charred lemon juice.
Arrange a few slices of steak on a plate, then top with the sauce and serve the potato salad alongside.