preheat broiler and place rack 6 inches from heat source.
In small bowl, mix pesto with water.
Spray 15½” by 10½” jelly-roll pan with nonstick cooking spray.
Arrange onion slices on pan; brush with 2 tablespoons pesto mixture.
Broil onion slices 5 minutes.
Arrange peppers on pan with onion; broil 12 to 15 minutes longer or until vegetables are tender, turning vegetables over halfway through cooking.
Meanwhile, with meat mallet, pound chicken placed between two sheets plastic wrap to even ½-inch thickness; season with salt and pepper.
In 12-inch skillet, heat oil over medium heat until hot.
Add chicken and cook 6 to 8 minutes or until browned on both sides, turning over once.
Top chicken in pan with mozzarella slices; cover and cook 2 to 3 minutes or until cheese melts and chicken is no longer pink throughout; chicken should register 165°F when instant-read thermometer is inserted horizontally into center.
To serve, on each dinner plate, stack 1 slice onion, 2 slices pepper, 1 slice tomato, and 1 piece chicken with mozzarella; drizzle with remaining pesto mixture.