Preheat the oven to 425 degrees. Line an 18 x 13-inch large, rimmed sheet pan with foil or parchment and spray with oil.
In a small bowl, combine 3 tablespoons of the mustard, 2 tablespoons of the maple syrup, and the soy sauce.
Season both sides of the chicken with 1/2 teaspoon of the salt and pepper to taste, then arrange it on the prepared pan.
In a large bowl, combine the Brussels sprouts, butternut squash, thyme, and olive oil, and the remaining 1/4 tsp. salt. Season with pepper and toss well.
Arrange the vegetables on the prepared sheet pan in a single layer around the chicken. Pour the Dijon-maple sauce over the chicken, turning to coat completely, and pour any remaining sauce over the vegetables.
Bake until the chicken is cooked through and the vegetables are tender, about 40 minutes.
Meanwhile, in a small bowl, whisk together the remaining 1 tablespoon each mustard and maple syrup.
Brush the mustard/maple mixture over the chicken. Bake for 5 more minutes, until brown, and serve right away.