Cut away duck backbones and discard. Cut off first 2 joints of each wing and reserve. Cut ducks into quarters. Remove any fat. Pat duck pieces dry with paper towels. Pierce skin all over with fork. Season with salt and pepper. Heat vegetable oil in heavy large Dutch oven over medium-high heat. Working in batches, add duck quarters, skin side down, and cook until golden, about 8 minutes. Turn and cook 3 minutes longer. Transfer to large bowl. Add wings and giblets to Dutch oven and cook until golden, turning frequently, about 10 minutes. Using slotted spoon, transfer to another bowl. Pour off all but 2 tablespoons duck fat from Dutch oven. Add onions, carrots, parsley stems, thyme and bay leaf to Dutch oven. Cover and cook until vegetables are tender, stirring occasionally, about 10 minutes. Add 3 1/2 cups broth, wine, giblets and wings. Cover and simmer 30 minutes. Strain liquids and return to pot. Add duck quarters; bring to boil. Reduce heat, cover partially and simmer until cooked through, turning occasionally, about 40 minutes. Transfer duck to plate. Cook turnips in large pot of boiling salted water until just tender, about 25 minutes. Drain; cut into quarters. Combine 1/4 cup chicken broth and cornstarch in small bowl and whisk to blend. Skim fat from duck cooking liquid. Boil liquid until reduced to 2 1/2 cups, about 10 minutes. Add cornstarch mixture and whisk until sauce thickens slightly. Add duck and turnips. Reduce heat, cover and simmer until duck and turnips are heated through, about 7 minutes. Season with salt and pepper. (Can be made 1 day ahead. Cover; chill. Rewarm over medium heat.) Transfer to large bowl. Top with minced parsley.