1. Preheat oven to 475°.
2. Combine mustard and 1/2 teaspoon thyme in a small bowl. Sprinkle chicken with 1/4 teaspoon salt. Heat a skillet coated with cooking spray over medium-high heat. Add chicken, skin side down; cook 5 minutes or until browned. Turn and cook an additional 3 minutes or until lightly browned. Remove chicken; spread mustard mixture evenly over skin side of each breast.
3. Combine potato, carrot, onion, oil, 1/2 teaspoon thyme, 1/2 teaspoon salt, and pepper. Place on a broiler pan coated with cooking spray.
4. Bake at 475° for 10 minutes. Stir potato mixture; place chicken, skin side up, over potato mixture. Bake an additional 15 minutes. Sprinkle with parsley.