Heat the oven to 400 degrees f. and line a large baking sheet with parchment paper.
In a large glass bowl, stir together parmesan, crushed corn flakes, garlic powder, oregano, and cayenne pepper.
In a separate bowl combine chicken with 2 Tablespoons oil, sea salt, and pepper. Stir well to coat.
Dip chicken breasts in the cornflake mixture and gently press to coat on all sides, then place onto the prepared baking sheet.
Toss sliced zucchini and tomatoes with remaining 1 Tablespoon oil.
Make some space on the sheet pan as shown between the chicken, then evenly add the zucchini and cherry tomatoes.
Bake for 15-17 minutes in your preheated oven, or until chicken is cooked through and veggies are crisp-tender.