Nutrition per serving may change if servings are adjusted.
6 cups cubed peeled butternut squash (2 lbs.)
4 cups broccoli florets
3 tablespoons olive oil, divided
1 tablespoon chopped fresh thyme or 1 tsp. dried, divided
½ teaspoon salt, divided
½ teaspoon ground pepper, divided
1 pound boneless, skinless chicken breast, cut into 2-inch strips
½ medium onion, finely chopped
3 cloves garlic, minced
¼ cup low-sodium chicken broth
¼ cup Dijon mustard
2 tablespoons dry white wine (optional)
¼ cup grated Parmesan cheese
1 tablespoon chopped fresh parsley
Position racks in upper and lower thirds of oven; preheat to 400°F.
Combine squash, broccoli, 1½ Tbsp. oil, 1½ tsp. fresh thyme (or ½ tsp. dried), and ¼ tsp. each salt and pepper on a large rimmed baking sheet; toss to coat. Roast on the lower rack for 15 minutes.
Arrange chicken in a single layer on another large rimmed baking sheet. Drizzle with ½ Tbsp. oil and the remaining ¼ tsp. each salt and pepper; toss to coat. After the vegetables have roasted for 15 minutes, stir them and return to the oven. Place the pan of chicken on the upper rack. Roast both pans until the vegetables are browned and tender and the chicken is cooked through, 14 to 18 minutes more.
Meanwhile, heat the remaining 1 Tbsp. oil in a small saucepan over medium heat. Add onion and cook, stirring often, until softened, 3 to 4 minutes. Add garlic; cook, stirring, until fragrant, about 30 seconds. Add broth, mustard, and wine (if using); simmer, stirring often, until slightly reduced, 2 to 3 minutes. Stir in Parmesan, parsley, and the remaining 1½ tsp. fresh thyme (or ½ tsp. dried).
Divide the chicken and vegetables among 4 plates and serve with the sauce.