Preheat oven to 450F
You'll need five to six pounds of turkey parts (ideally a mix of necks, wings, and legs) to make enough gravy for 10 to 12 people. Ask your butcher to chop the parts into four-inch pieces; smaller pieces are best because the skin and collagen release more easily from the bones, adding flavor and body to the broth.
Pat the parts dry with paper towels, arrange them in a single layer in a large flameproof roasting pan (I use the same one I use for the turkey). If they don't fit in a single layer, use a second roasting pan (I use a glass lasagna pan). Drizzle the oil on and mix around a bit just so the turkey gets very lightly coated.
Roast turkey parts, flipping them with tongs after 30 minutes, for an hour total, until nicely browned. For the last 20 minutes of roasting, add the carrots, onion and celery to the pans.
Transfer the roasted turkey and vegetables to a large stockpot. Don't worry if bits stick; you'll get them when you deglaze the pan. Add 2 cups of very hot tap water to the pan (or recently boiled water) and scrape the bottom with a wooden spoon to dissolve any cooked-on drippings. Pour the liquid into the stockpot. Do this for both pans, if using two. Note: If the bits don't come off easily enough, put the burners on the stovetop and boil the water while scraping. I usually don't find this necessary).
Add enough additional water to the stockpot to just cover the turkey pieces; any more can result in a diluted broth. Depending on the shape and size of your pot and turkey parts, you'll probably need about seven to eight cups of water total. Add salt, peppercorns, garlic, thyme, parsley and bay leaves.
Over medium high heat, bring to just below a boil, then immediately lower the heat to a very gentle simmer. Be careful to not let the broth boil aggressively, so it will be clear. Continue to simmer, uncovered, until it has a sweet, rich turkey flavor, two and a half to three hours. If it reduces too much, you can add a little more water to top it up.
When the broth is done, gently remove the large pieces of turkey and vegetables with a slotted spoon and discard. Set a fine-mesh strainer over a heat-proof bowl. (If you don't have a fine-mesh strainer, line a colander with a double thickness of cheesecloth.) Strain the broth, pushing very gently on any remaining solids to extract as much liquid as you can but don't mash the vegetables—this will cloud the stock and give it a murky flavor. Don't try to remove the fat now, it will be much easier when the stock has cooled.
Let the broth sit on the counter until it cools to room temperature, and then cover and refrigerate it. Once the broth has completely chilled, remove the layer of surface fat. You can keep it refrigerated for up to four days or freeze it for up to six weeks.