Preheat oven to 350°F (175°C).
Pat the 4 chicken breasts dry with paper towels. Evenly sprinkle the chicken with 1/4 teaspoon of the kosher/sea salt and 1/4 teaspoon of the black pepper.
Pour the 2 beaten eggs into a shallow bowl. Dip each chicken breast into the eggs, letting any excess egg drip off.
Spread the 1/2 cup grated Parmesan on a plate. Press each egg-coated breast into the Parmesan, coating both sides.
In a large bowl, combine the sliced zucchini, sliced yellow squash, sliced garlic, halved cherry tomatoes, and the thyme (use 1 tablespoon fresh thyme leaves or 1 teaspoon dried thyme). Add the remaining 1/4 teaspoon salt, remaining 1/4 teaspoon black pepper, and the 2 tablespoons extra virgin olive oil. Toss to coat evenly.
Spread the tossed vegetables in an even layer across the bottom of a 13 x 9-inch baking dish. Arrange the Parmesan-coated chicken breasts on top of the vegetables.
Bake uncovered for 35 to 40 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the vegetables are tender.
Remove from the oven and let rest 3–5 minutes. Serve the chicken on top of or alongside the vegetables.