01 - Preheat oven to 400°F. Lightly grease a 9x13-inch casserole dish with cooking spray or butter.
02 - In a large bowl, combine chicken pieces, squash, Brussels sprouts, carrots, parsnips, leeks, and garlic. Toss thoroughly to distribute evenly. Spread mixture in the prepared casserole dish.
03 - Whisk together chicken broth, heavy cream, Dijon mustard, cornstarch, thyme, rosemary, black pepper, and salt in a mixing bowl until smooth and well combined.
04 - Pour sauce evenly over the chicken and vegetables. In a small bowl, combine cheese, breadcrumbs, and olive oil. Sprinkle mixture uniformly over the casserole.
05 - Cover casserole loosely with aluminum foil. Bake for 30 minutes to allow vegetables to begin softening and chicken to start cooking through.
06 - Remove foil and continue baking for 20 minutes until vegetables are tender, chicken reaches internal temperature of 165°F, and topping is golden brown and crispy.
07 - Let casserole rest for 5-10 minutes before serving to allow flavors to meld and sauce to thicken slightly. Garnish with fresh herbs if desired.