Spread 1 side of each bread slice evenly with 2 tablespoons pizza sauce. Layer each of 4 bread slices with 1 cheese slice, 1 tablespoon bell pepper and 12 pepperoni slices. Top with remaining cheese and bread slice, sauce side down; press sandwich together slightly. Brush outside of sandwiches lightly with oil.
Preheat panini grill according to manufacturer’s instructions. Cook sandwiches 3 minutes or until browned and cheese melts.
Skillet Cooking: Place sandwiches in large skillet over low heat. Cook, covered, 3 to 5 minutes per side or until browned and cheese melts, pressing down with spatula to slightly compress.