Rub steak with 2 Tbsp. oil; season generously with salt and pepper. Let sit at room temperature 30 minutes.
Prepare a grill for medium-high heat; oil grill grate. Grill steak to desired doneness, 5–7 minutes per side for medium-rare. Let rest 5 minutes before slicing against the grain.
Meanwhile, toss parsley, Parmesan, lemon juice, and remaining 1 Tbsp. oil in a medium bowl; season with salt, pepper, and more lemon juice, if desired. Serve steak topped with parsley-Parmesan salad.