Heat oven to 450 degrees F. Coat a large baking pan with cooking spray.
Place parsnips, carrots and potatoes in a large bowl. Toss with olive oil, salt, pepper and rosemary. Spoon into the prepared pan and roast at 450 degrees F. for 35 minutes, turning after 15 minutes.
Heat a large nonstick skillet over medium-high heat. Add 1 tablespoon oil. Coat chicken in flour and add half to skillet. Cook 2 minutes per side. Remove to a plate and repeat with remaining tablespoon oil and chicken. Remove chicken to plate.
Reduce heat to medium and pour cider into skillet. Cook 1 minute, scraping up any browned bits from pan. Stir in mustard, thyme, salt and pepper. Add chicken and simmer on medium-low, covered, for 4 minutes.
Spoon sauce over chicken. Serve with the roasted vegetables.