Spread toasted side of each English muffin half with pesto. Spread cheese over 4 English muffin halves; top with tomato slices, radicchio, and remaining English muffin halves.
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 2 cans. Cook 2 minutes. Flip, replace weight, and cook 2 minutes more.