Preheat an outdoor grill for medium heat; lightly oil the grate.
Place basil, oil, garlic, Romano cheese, oregano, and pepper into a blender. Blend on high until smooth, adding additional oil if necessary, about 30 seconds.
Grill chicken until juices run clear, about 5 minutes per side. Do not turn off grill.
Spoon 1 tablespoon of Caesar dressing onto 2 slices of bread. Top each with lettuce, and an additional slice of bread. Spread the second slice of bread thickly with the pesto. Top each sandwich with a cooked chicken breast, a slice of smoked mozzarella, and the remaining bread.
Grill sandwiches until the cheese is melted, and the bread is toasted, about 3 minutes per side.
