Light a hot fire in a grill or preheat the oven to 350°. In a large bowl, combine the bread crumbs with the parsley, Fontina, olives, Parmesan, 2 tablespoons of olive oil and 1 tablespoon of thyme.

Lay the steak on a work surface with a short edge facing you. Press one hand flat on the meat to steady it. Using a long, sharp knife, make a horizontal cut in a long side of the steak to within 1/2 inch of the opposite edge. Open the flank steak like a book.

Cover the cut side of the steak with the prosciutto slices, then top with a layer of basil leaves. Spread the bread crumb mixture on top. Starting with the side facing you, tightly roll up the steak around the filling. Using kitchen string, tie the roll in 4 or 5 places.

In a small bowl, combine the remaining 1 tablespoon of olive oil and 2 teaspoons of thyme with the salt, garlic and pepper. Rub this mixture all over the rolled steak.

Bank the coals to one side of the grill or turn off one side of the grill. Grill the steak over high heat until browned all over, 8 to 10 minutes; turn the steak 4 times as it cooks. Move the meat away from the direct heat and grill for 15 to 20 minutes, or until an instant thermometer registers 120° to 125° for medium rare. Alternatively, heat a large ovenproof skillet. Add the rolled steak and cook over moderately high heat until browned all over 8 to 10 minutes. Transfer the skillet to the oven and roast the steak for 20 to 30 minutes, or until an instant thermometer registers 120° to 125° for medium rare. Transfer the rolled steak to a carving board, cover loosely with foil and let rest for 10 minutes. Discard the strings and slice the steak crosswise 1/2 inch thick. Serve.