01 - Preheat oven to 400°F. Lightly grease a 9x13-inch casserole dish with cooking spray or butter.
02 - Place chicken pieces, butternut squash, Brussels sprouts, carrots, parsnips, leeks, and garlic in a large bowl. Toss gently to combine, then spread evenly 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 cornstarch is fully dissolved.
04 - Pour the sauce evenly over the chicken and vegetables in the casserole dish, ensuring all ingredients are coated.
05 - Combine grated cheese, breadcrumbs, and olive oil in a small bowl. Mix until crumbly, then sprinkle evenly over the entire casserole.
06 - Cover casserole loosely with aluminum foil. Bake for 30 minutes to begin cooking vegetables and chicken through.
07 - 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.
08 - Let casserole rest for 5-10 minutes before serving to allow sauce to thicken slightly. Garnish with fresh thyme or rosemary if desired.