Melt 1 tbsp butter in a Dutch oven over medium-high heat. Sprinkle chicken evenly with salt and pepper. Add chicken to dutch oven; saute 5 minutes on each side or until browned. Remove from pan.
Add broth to pan; cook 1 minute, scraping pan to loosen browned bits. Add wine, thyme, turnips, carrots, onions,6 parsley sprigs, and bay leaves; stir. Add chicken to pan, nestling into vegetable mixture; bring to a boil.
Cover, reduce heat, and simmer 20 minutes or until chicken is done. Discard bay leaves and parsley sprigs. Remove chicken and vegetables from the pan.
Place a zip top plastic bag inside a 2 cup glass measure. Pour cooking liquid into bag. Let stand 10 minutes (fat will rise to the top). Seal bag; carefully snip off 1 bottom corner of bag. Drain drippings back into the pan, stopping just before fat layer reaches opening; discard fat.
Return liquid to pan. Bring liquid to a boil; cook until reduced to 1 1/2 cups (about 5 minutes.
Melt remaining 1 tbsp butter in a small skillet. Add flour, stirring until smooth. Add flour mixture to cooking liquid; cook 2 minutes or until slightly thick, stirring constantly.
Return chicken and vegetable mixture to pan; stir in peas. Cook 3 minutes or until thoroughly heated. Garnish with chopped parsley.