Stir together cheddar, mayo, pimientos, cumin, chili powder, and cayenne in a bowl. Spread cheese mixture on six slices of bread; top with zucchini and remaining bread slices.
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.