Heart is probably the most accessible of organ meats. It may be daunting in appearance, but it's meaty and firm and cooked, and tastes very good. It is prepared in this manner in various corners of Lazio, Umbria, and Tuscany. Most butchers will special-order veal heart for you.
Adapted from “The Country Cooking of Italy” by Colman Andrews (to be published in Fall 2011 by Chronicle Books).
Combine the oil and lemon juice in a non-reactive bowl or baking dish, and then marinate the veal hearts for 2 hours at room temperature, turning them several times.
Light the grill, letting coals or wood get very hot (if using a gas grill, preheat to at least 500 degrees F/260 degrees C).
Remove the heart halves from the marinade and lightly blot off excess oil with paper towels. Season them generously on both sides with salt and pepper, and then grill them for 5-6 minutes total, turning them once.
To serve, cut the meat into thin slices across the grain. Drizzle a little olive oil over the slices.