This flank steak can be served either warm or at room temperature. We suggest setting out a basket of thinly sliced rustic bread, so guests can make sandwiches if they like.
Let steaks sit at room temperature 1 hour. Heat grill to medium-high. Pat steaks dry. Brush with 2 tablespoons oil, and season liberally with salt and pepper. Grill 7 to 8 minutes per side (or until internal temperature reaches 135 degrees) for medium-rare. Let steaks rest, loosely tented with foil, 10 minutes.
Meanwhile, mix together olives, peperoncini and their juice, parsley leaves and stems, oregano, and remaining 2/3 cup oil. Sauce can be made 1 day in advance and refrigerated; bring to room temperature before serving.
Thinly slice steaks against the grain; arrange on a platter. Spoon half the sauce on top; serve remaining sauce on the side.