Lightly brush sandwich bread with olive oil; turn slices, oiled sides down. Top half the bread with half the cheese; season with salt and pepper. Spread pesto or tapenade over cheese, then top with peppers and remaining cheese and bread.
Heat a large grill pan or skillet over medium heat. Place sandwiches in pan (work in batches, if needed); weight with a heavy skillet. Cook over medium-low heat, pressing down firmly with skillet, until bread is golden and cheese is melted, 6 to 8 minutes per side. Serve warm.