How to Make It
Place a rimmed baking sheet on rack in center of oven; preheat to 425°F. Pat chicken dry. Combine paprika, chili powder, and 1/4 tea - spoon each of the salt and pepper in a small bowl; rub evenly over chicken. Place potatoes, brussels sprouts, and shallots in a medium bowl. Add thyme, 2 tablespoons of the oil, ½teaspoon of the salt, and remaining 1/4 teaspoon pepper; toss to coat.
Remove baking sheet from oven; mist with cooking spray. Place vegetables on 1 half of hot baking sheet and chicken on other. Roast until chicken is cooked through and vegetables are tender and slightly charred, 15 to 18 minutes. With pan still in oven, adjust temperature to high broil; cook until vegetables are charred and chicken is slightly crisp, 3 to 4 minutes.
Meanwhile, whisk together vinegar, mustard, honey, and remaining 1/4 teaspoon salt in a bowl. Slowly whisk in remaining 3 tablespoons oil. Drizzle chicken and vegetables with vinaigrette. Sprinkle with parsley.