1. Preheat grill with medium-high flame.
2. Wipe mushroom caps clean. With a spoon, scoop out gills; discard. Place caps on plate.
3. In a small bowl, whisk together olive oil, vinegar, oregano, salt and pepper. Brush both sides of mushrooms with vinaigrette.
4. Grill mushrooms 2-3 minutes per side. Remove to plate; tent aluminum foil over plate to keep warm.
5. To assemble sandwiches, spread pesto on one side of each slice of bread. On a large platter, place 4 prepared bread slices. Place 1 mushroom cap on each slice; top each with 1 mozzarella slice, roasted red bell pepper and lettuce leaf. Top with remaining prepared bread slices.
6. Secure each sandwich with 2 toothpicks and slice diagonally, if desired. Serve warm with arugula salad and sweet potato chips, if desired.