Heat a large cast-iron skillet or stovetop grill pan over medium heat. Spread 4 pieces of the bread with 1 tablespoon of the pesto each. Layer each piece with equal amounts of the mozzarella slices, chicken, and red peppers. Add a light film of olive oil to the pan; when hot, cook the sandwiches (2 at a time, if necessary) until the bread is crispy and the cheese is melted, 3 to 4 minutes each side. (For the best results, use a heavy pan to weigh down the sandwiches.)