Preheat the oven to 400 degrees F. Lightly coat a large baking sheet with nonstick spray. Arrange the carrots, broccoli, and red onion on the baking sheet.
In a small bowl or measuring cup with a spout, whisk together the olive oil, maple syrup, mustard, garlic, salt, pepper, oregano, and thyme. Drizzle about 3 tablespoons over the veggies, reserving the rest. Toss the veggies to coat with the mixture, then spread them into a single layer. Arrange the pounded chicken breasts on top.
Add the balsamic vinegar to the reserved olive oil/maple syrup mixture and whisk to combine. Brush over the tops of the chicken breasts.
Place the baking sheet in the oven and roast until the chicken is cooked through and reaches an internal temperature of 165 degrees F, about 20-30 minutes, depending upon the size of your chicken breasts (mine were about 11 ounces each and cooked in 28 minutes). Remove to a plate, cover, and let rest for a few minutes. If the vegetables are not as brown as you would like, return them to the oven for a few minutes to continue cooking. Sprinkle with fresh parsley and enjoy warm.
Notes
TO STORE: This recipe is best enjoyed the day it's prepared. However, leftovers may be stored in the fridge for up to three days.
TO REHEAT: For best results, warm the vegetables to crisp them back up in a 350 degree F oven. I found that reheating chicken breasts tends to dry them out. If you must, do so in a pan with a bit of water for extra moisture. Or enjoy the chicken breasts at room temperature atop greens for a quick and delicious salad.