Remove giblets and neck from turkey cavity; set aside in the refrigerator for Step 4. (Discard liver or freeze for another use.) Place the turkey in a large roasting pan and pat dry with paper towels. Rub salt all over the turkey, including inside the cavity. Refrigerate, breast-side up and uncovered, for 24 hours.

Position rack in lower third of oven; preheat to 500 degrees F.

Set a rack in the pan and place the turkey on it, breast-side up. Brush the turkey with oil. Transfer to the oven and reduce the temperature to 325 degrees F. Roast the turkey until an instant-read thermometer inserted into the thickest part of the breast and the innermost part of the thigh registers 165 degrees F, 2 to 2 1/2 hours.

Meanwhile, combine water, celery, onion, carrot, bay leaves and thyme with the reserved giblets and neck in a large saucepan. Bring to a simmer over medium heat. Reduce heat to maintain a bare simmer and cook, uncovered and skimming occasionally, until the stock is well flavored, about 2 hours. Remove from heat and pour the stock through a sieve into a large measuring cup. (Discard the solids.) If necessary, add enough water to make 3 cups.

Transfer the turkey to a large cutting board and tent loosely with foil. To prepare gravy, carefully pour the drippings from the roasting pan into a fat separator, leaving about 2 tablespoons of drippings in the pan. Set the pan over 2 burners on medium heat. Add 1 cup of the stock and cook, scraping up any browned bits with a wooden spoon, until the liquid is slightly reduced, about 1 minute. Add flour and cook, stirring constantly, until thickened, about 2 minutes. Add the remaining 2 cups stock and the defatted drippings; cook, stirring occasionally, until the gravy is thick and smooth, about 5 minutes. Strain the gravy through a fine-mesh sieve.

Carve the turkey and serve with the gravy.