Adapted from Anne Quatrano's "Summerland: Recipes for Celebrating with Southern Hospitality" (Rizzoli).
Combine giblets, celery, onion, and 6 cups water in a large pot. Bring to a boil over high heat, then reduce heat to low and simmer, uncovered, 1 hour. Pass mixture through a fine sieve. Reserve stock and giblets; discard other solids.
Tilt roasting pan and skim fat from top with a spoon, or pour drippings into a fat separator. Combine 1/2 cup fat (add melted butter as needed to reach 1/2 cup) with flour in a small saucepan. Cook over medium heat, stirring frequently, until mixture becomes nutty and golden and has texture of wet sand, about 5 minutes. Remove from heat.
Place roasting pan across 2 burners over medium heat; stir reserved stock into drippings. Bring to a simmer, stirring and scraping up browned bits. Slowly add flour mixture, whisking constantly to prevent lumps from forming. Reduce heat to low and simmer until thickened to desired consistency. Pass gravy through a fine sieve; finely chop reserved giblets and stir into gravy. Season with salt and pepper.
If you prefer a smooth gravy, simply discard the giblets after straining the stock.
You can also use the pan drippings from our Roasted Heritage Turkey with Aromatic Brine recipe to make this flavorful gravy.