Heat the oil in a large soup pot over medium-high heat. Add the turkey neck and giblets and cook, turning occasionally, until well browned, about 10 minutes. Add the onion, celery, and carrot and cook, stirring occasionally, until the onion softens, about 5 minutes. If using the wings, add them to the pot at this point, but no need to brown them. Add the broth and enough cold water to cover the turkey parts by 1 inch. Bring to a boil over high heat, skimming off any foam that rises to the surface. Add the parsley, thyme, peppercorns, and bay leaf. Reduce the heat to low. Simmer, uncovered, until the stock is full-flavored, about 3 hours. Strain through a wire sieve into a bowl. You should have about 2½ quarts broth; add more chicken broth or water, if necessary. Cool completely. Cover and refrigerate overnight.