Preheat oven to 425 °F. Prepare outdoor grill or grill pan to medium-high heat.
Unroll steaks on a large work surface and lightly pound if necessary to make the meat an even thickness, about ¼- to ½-inch thick. Drizzle meat with EVOO and season both sides with salt and pepper. Scatter the zest of 1 lemon on each steak. Halve the zested lemons for grilling and reserve. Top the meat with rosemary and chopped garlic, and scatter a layer of parsley over the top using about 1 cup of leaves per steak. Top the parsley with shaved Parmigiano-Reggiano cheese.