Purée the ingredients for the basil pesto in a food processor. Set aside.
Add chicken and mushrooms to sheet pan. Spray with zero-calorie nonstick cooking spray and toss with 2 Tbsp of pesto, seasoning with salt and pepper to taste. Bake in oven for 8 minutes. Remove from oven and drain excess liquid.
Add red pepper, broccoli, and zucchini, tossing with 2 Tbsp of pesto. Bake another 8 minutes until chicken is fully cooked.