Attach 4 or 5 rosemary sprigs to a wooden spoon handle with twine or a rubber band to form a basting brush.
In a small saucepan, combine the oil, garlic and a few small pieces of rosemary; heat over low heat to infuse the oil.
Let the steaks come to room temperature and season liberally with salt and pepper.
Heat a grill to high heat. If making a charcoal or wood fire, bank the coals to one side to intensify the heat and provide a cook side where you can rest the meat. (As an alternative to grilling, heat a large, cast-iron skillet over high heat and preheat the oven to 325°F).
Grill the steaks for 6-7 minutes per side, turning once and basting frequently with the garlic-rosemary oil, until the meat reaches 125°F on a meat thermometer. Pull meat off the heat and let rest for 10 minutes before slicing.
(If cooking indoors, brown the steaks in the preheated skillet for 4 minutes on each side and the edges. Transfer the skillet to the oven and cook until the meat reaches 125°F, 6-8 minutes more. Transfer the meat to a carving board and let rest for 10 minutes.)
Drizzle the cut lemons with oil and season with salt and pepper. Grill, cut side down, on the grill or in the skillet until caramelized, 4-5 minutes.
For the parsley sauce, combine the parsley, rosemary, garlic, lemon zest, lemon juice, anchovies, Worcestershire sauce, oil, salt and pepper in a food processor or blender. Purée into a sauce.
Carve the filet and sirloin off the bone and, working perpendicular to the bone against the grain of the meat, cut into 1/2-inch thick slices. Douse the meat with the juice from the charred lemon.
To serve, arrange a few slices of steak on each plate and spoon a generous strip of parsley sauce across them.