Remove the turkey liver from the giblets so your broth won't become bitter. To cool the broth quickly, set the bowl in an ice-water bath and stir it occasionally.
Heat oil in a large Dutch oven over medium-high heat. Add turkey wings, giblets, and neck; sauté 15 minutes or until well browned. Cover and reduce heat to low; cook 5 minutes. Stir in onion and celery; cover and cook 10 minutes, stirring occasionally. Add 8 cups water; bring to a boil. Cover, reduce heat, and simmer 30 minutes. Strain broth through a fine sieve into a large bowl; discard solids. Cool to room temperature. Cover and chill 8 hours or overnight. Skim solidified fat from surface of broth; discard.