Take your whole heart and, with a sharp knife, go over both sides of it removing any sinewy parts including skin and tendons. You should be left with a uniform piece of meat that resembles a very lean steak.
Cut the heart steak into 1/2 inch slices. Drizzle on some olive oil and season well with salt and pepper.
Grill heart strips on high heat for about 3 minutes per side for medium rare. Once the steaks come off the grill, let them rest for a few minutes before serving. Cover them with foil to keep them warm.
Mix gremolata ingredients together ahead of time and let sit at room temperature for a few minutes (30 would be good).
Serve a few heart strips over a starch (like polenta). Top with gremolata.