Preheat the oven to 350°F (175°C) and lightly coat a 9x13-inch casserole dish with nonstick spray.
In a medium bowl, combine the zucchini, yellow squash, red bell pepper, and quartered potatoes.
Drizzle the vegetables with 1 tablespoon olive oil and season with half of the salt and half of the pepper. Add 1/4 cup of the panko, 2 tablespoons of the grated Parmesan, and 1 teaspoon of the garlic powder; toss to coat evenly.
Spread the seasoned vegetables in an even layer in the prepared casserole dish.
Rinse the chicken breasts and pat dry. Season both sides with the remaining salt and pepper.
Place the 2 egg whites in a small bowl and whisk briefly. In a second small bowl, mix the remaining panko, the remaining Parmesan (about 1/4 cup), and the remaining 1 teaspoon garlic powder.
Dip each chicken breast into the egg whites, then press into the panko-Parmesan mixture to coat all sides. Lay the coated chicken on top of the vegetables in the casserole dish.
Bake for 30 to 40 minutes, or until the chicken is cooked through (internal temperature 165°F/74°C) and the vegetables are tender.
Remove from the oven, sprinkle with any remaining Parmesan, and serve immediately.