Preheat oven to 400 F. Line roasting dish with parchment paper.
In bowl, toss parsnips with 1 Tbsp oil, rosemary, thyme, 1/4 tsp salt, and 1/4 tsp pepper. Spread into parchment-lined roasting dish.
Season chicken with remaining 1/4 tsp salt and 1/4 tsp pepper. In large skillet over medium-high, heat remaining 1 Tbsp oil and sear chicken, skin side down, until golden and crisp. Flip and nestle into parsnips on roasting dish. Roast in preheated oven for 25 to 30 minutes, or until chicken is cooked through. Remove chicken and parsnips and add to serving plate.
To skillet, over medium-low heat, add apple cider vinegar, scraping up brown bits. Whisk in mustard and butter to create glossy sauce. Spoon over chicken and serve.