Brown the giblets, turkey neck, and backbone if you have it, in melted butter over medium heat. Give the pieces a few minutes on each side until they pick up real color, not just gray to light brown; that browning is where the flavor comes from, not the simmering that follows. Do not rush this step. A pale sear here means a flat-tasting gravy later, and there is no fixing that once the broth is simmering.
Turkey giblets, Turkey neck, 2 tablespoons Butter
Add the chopped onion, celery, carrot, and herbs, then cover everything with water. Let it bubble gently, not boil hard, on low heat while your turkey finishes roasting; a hard boil clouds the broth and toughens the neck meat. You want a broth that smells rich and tastes seasoned on its own before you ever strain it.
4 Cups Water, 2 Stalks celery, 2 Large Carrots, 1 medium onion, 2 each Bay Leaves, ¼ Cup Parsley, 3 springs Rosemary, 8-10 leaves sage, salt and pepper
Once your turkey comes out to rest, whisk flour directly into the hot drippings left in the roasting pan. Keep whisking over the heat until the mixture turns a light golden color and smells toasted rather than raw; that color change is what cooks out the starchy flour taste.
3 Tablespoons Flour, All Purpose, Drippings from roasted turkey
Chop the giblets finely, strain your broth to remove the solids, and whisk the strained broth into the roux a little at a time. Let the gravy simmer until it coats the back of a spoon. If you pour all the broth in at once instead of whisking it in gradually, you risk lumps you cannot smooth back out.
Pour the finished gravy into a warmed gravy boat so it stays hot longer at the table. Pour, pass, and let people go back for seconds.