Preheat the oven to 350°F (175°C) and lightly coat a 9x13-inch casserole dish with non-stick spray.
In a mixing bowl, combine the zucchini, yellow squash, red bell pepper, and quartered red potatoes.
Add 1 tablespoon olive oil, 1/2 teaspoon kosher salt, 1/4 teaspoon black pepper, 1/4 cup of the panko, 2 tablespoons grated Parmesan, and 1 teaspoon garlic powder to the vegetables; toss until evenly coated and spread them in an even layer in the prepared casserole dish.
Rinse and pat the chicken breasts dry, then season both sides with the remaining kosher salt and black pepper.
Place the 2 egg whites in a small bowl and whisk lightly. In a second small bowl, combine the remaining panko, the remaining grated Parmesan, and the remaining 1 teaspoon garlic powder.
Dip each chicken breast in the egg whites, then press into the panko-Parmesan mixture to coat all sides; place the coated chicken on top of the vegetables in the casserole dish.
Bake in the preheated oven for 30 to 40 minutes, until the chicken is cooked through (no pink inside) and the vegetables are tender.
Remove from the oven, sprinkle with any remaining grated Parmesan, and serve.