- Cut squash diagonally into 1/2-inch thick slices. Toss with oil and chile flakes; season to taste with salt and freshly ground black pepper.
- Arrange in one layer in preheated panini pan. Close press; cook 3 minutes or until squash is seared and tender.
- Slice off the tops of the ciabatta rolls; save for another use. The rolls should now be 1-inch thick. Split the rolls horizontally. Turn bottom halves up and top with 2 slices cheese, squash mixture, mint and remaining cheese.
- Close sandwiches with top halves of ciabatta rolls. Brush lightly with additional olive oil, if desired.
- Cook sandwiches in preheated panini maker or on gas grill for 4 to 5 minutes, turning once, until cheese is melted and bread is golden brown.