Cover a large cutting board with a sheet of plastic wrap, lay the chicken on top, then stretch a second sheet of plastic wrap across the top. Lightly pound the chicken breasts to an even 1/2-inch thickness (this will help them cook more quickly and evenly). Uncover the chicken and discard the plastic. Sprinkle the chicken with 1/2 teaspoon kosher salt and place in a large ziptop bag.
In a large measuring cup or mixing bowl, whisk together the olive oil, balsamic vinegar, Italian seasoning, garlic powder, black pepper, and remaining 1/2 teaspoon salt. Pour half of the mixture into the ziptop bag (watch for spills). Seal the bag, removing as much air as possible. Gently "squish" and turn the bag so that the chicken is evenly coated with the marinade, then lay the bag flat in a baking dish to catch any drips. Place in the refrigerator to marinade for 30 minutes or up to 8 hours.
While the chicken marinates, prepare the vegetables. Leave the tomatoes whole. Cut the zucchini into 3/4 inch dice (you can leave the peels on). Trim the ends off of the green beans. As you cut, place the vegetables in a second ziptop bag. Pour in the remaining balsamic mixture, seal, and place in the refrigerator with the chicken.
When you are ready to cook, preheat your oven to 425 degrees F. Remove the chicken and veggies from the refrigerator and let stand at room temperature while the oven heats. Generously coat a large, rimmed baking dish with nonstick spray or line with parchment paper or a silicone baking mat. Arrange the veggies around the edges of the pan and place the chicken in the center. The veggies can overlap a little, but make sure the chicken is not sitting on top of them.
Bake for 15 to 20 minutes, until the chicken reaches an internal temperature of 165 degrees F. The cooking time will vary based on the size of your chicken and how thinly you have pounded it. If the veggies are not as tender as you would like when the chicken is done, remove the chicken from the pan and transfer it to a plate and cover, cover it to keep it warm, then return the pan with the vegetables to the oven and continue baking until the vegetables are done to your liking. You may have some liquid on the pan that the vegetables have discarded (not a big deal! Just leave it behind when you serve). Sprinkle with the Parmesan and parsley. Enjoy hot.
Store leftovers in the refrigerator for up to 4 days. I like to rewarm the vegetables in a 350 degree F oven (line a baking sheet with foil and lightly coat it with nonstick spray, then place the veggies on top) and the chicken gently in the microwave or in a nonstick skillet on the stove. I recommend cutting the chicken into pieces first to help it reheat without drying out.
The leftover chicken is also delicious at room temperature, served over a salad.
Nutritional information is an estimate and was calculated with half of the marinade, as much of it is discarded prior to baking. If you would like to calculate it differently, you can do so for free at myfitnesspal.com.