How to Make It
Heat 1 tablespoon oil in a 10-inch cast-iron or other ovenproof skillet over medium-high. Sprinkle chicken with 1/2 teaspoon salt and 1/2 teaspoon pepper. Add chicken to pan; cook 6 minutes on each side. Place chicken on a cutting board; let stand 10 minutes. Shred into large pieces.
Preheat oven to 425°F.
Combine 2 1/2 cups stock and flour in a bowl, stirring with a whisk. Add remaining 1 tablespoon oil to pan. Add onion, carrot, and garlic; sauté 6 minutes. Add remaining 1/2 cup stock, scraping pan to loosen browned bits. Stir in turnip greens; cook 1 minute. Stir in remaining 1/2 teaspoon salt, remaining 1/2 teaspoon pepper, and flour mixture. Add turnips; bring to a boil. Reduce heat, and simmer 15 minutes or until vegetables are tender. Stir in chicken and parsley. Remove pan from heat.
Arrange piecrust over pan, folding edges under as needed. Cut slits in dough to allow steam to escape. Brush with egg white. Bake at 425°F for 20 minutes. Cool 10 minutes.