Layer avocado slices, tomatoes onion, and 1/2 cup spinach on each roll. Spray panini with cooking spray.
Coat skillet or grill pan with cooking spray, and heat over medium heat. Place panini in pan; weight with smaller diameter saucepan weighted with 1 or 2 cans. Cook 2 minutes, remove weight. Flip panini, replace weight, and cook 1 1/2 to 2 minutes more. (or cook 4 minutes in panini maker).