In a Dutch oven, brown turkey in oil. Add the celery, onion, salt, peppercorns and enough water to cover drumsticks. Bring to a boil. Reduce heat; cover and simmer for 20 minutes or until meat is tender. Remove drumsticks from broth; drain well. (Discard broth or strain and reserve for another use.)
Place drumsticks in a greased shallow roasting pan. Brush with half the preserves. Top with apricot halves; brush apricots with remaining preserves. Bake, uncovered, at 400° for 8-10 minutes or until glaze is set.