In a food processor or blender combine mayonnaise, 1/4 cup roasted pepper, and garlic. Cover and blend or process until nearly smooth.
Cut each roll in half horizontally; spread cut sides of rolls with mayonnaise mixture. On bottoms of rolls layer four roasted peppers (if desired), chicken, prosciutto, cheese, and mesclun mix. Replace tops of rolls. If desired, brush outsides of sandwiches with oil.
Preheat a covered indoor grill, panini grill, grill pan, or large skillet. Place sandwiches, half at a time if necessary, in grill. Cover and cook about 6 minutes or until rolls are lightly toasted and cheese is melted. (If using a grill pan or skillet, place sandwiches on grill pan or skillet. Weight sandwiches down with a heavy skillet. Cook over medium heat about 2 minutes or until rolls are lightly toasted. Turn sandwiches over, weight down, and cook about 2 minutes more or until rolls are lightly toasted and cheese is melted.)