Heat a grill pan over medium-high heat. In a large bowl, combine the mushroom, bell peppers, yellow squash and courgette. Drizzle with the oil, season with salt and pepper and toss to coat. Place the vegetables on the hot pan and grill until tender and lightly browned; use tongs to flip them once or twice during cooking. Transfer the vegetables to a plate.
Reduce the heat to medium. Spread one side of half the ciabatta pieces with Herbed Feta Spread and top each with one-fourth of the grilled vegetables and 1 lettuce leaf. Cover with the remaining pieces of ciabatta and brush the outsides of the sandwiches with oil. Place on the pan and grill, turning once, until the bread is browned and crisp and the cheese and vegetables are heated through, 8 to 10 minutes. If desired, place a cast-iron skillet on top of the sandwiches to press them while grilling. Serve warm.