1. Combine mayo and vinegar in small bowl. Spread on 4 slices of bread. Layer each slice with 1/4 of the chicken, 4 basil leaves, 1/4 of the roasted peppers, and 1 slice of cheese. Top with remaining bread slice.
2. Spray ridged grill pan with cooking spray and set over medium-high heat. Add sandwiches. Cover with heavy skillet filled with 1-2 soup cans. grill until the bread is will marked and the cheese is melted, about 3-4 minutes on each side.