Heat your oven to 425 degrees. Toss the turkey wings or necks with the olive oil, salt, and pepper and spread them on a large rimmed sheet pan in a single layer. Roast for 45 to 50 minutes, turning once halfway through, until the skin is deep golden brown and the pan has dark brown bits stuck to it. Those browned bits are where the flavor lives.

Transfer the roasted turkey parts to a large heavy saucepan or Dutch oven. Pour about 1 cup of the chicken broth onto the hot sheet pan and use a wooden spoon or spatula to scrape up all the browned bits. Pour that liquid and all the scrapings into the saucepan with the turkey.

Add the onion, celery, garlic, thyme, bay leaf, and remaining 4 cups of chicken broth to the pot. Bring it to a boil over medium-high heat, then reduce to a gentle simmer. Simmer uncovered for 45 minutes. The liquid will reduce and the broth will take on a rich turkey flavor. You should have about 3 to 3 1/2 cups of liquid after simmering.

Strain the liquid through a fine-mesh strainer into a large bowl or measuring cup. Press on the solids with the back of a spoon to extract as much flavorful broth as possible, then discard the solids. Skim the fat from the surface of the strained broth using a fat separator or a large spoon. Set the broth aside.

Wipe out the saucepan and return it to medium heat. Add the butter and let it melt. Once it is foamy, add the flour all at once and whisk constantly for about 2 minutes. The mixture will look like a pale paste, and that is what you want. Cooking the flour here removes the raw flour taste before any liquid goes in.

Slowly pour the strained turkey broth into the flour and butter mixture, about 1/2 cup at a time, whisking steadily after each addition to prevent lumps. Once all the broth is incorporated, bring the gravy to a gentle simmer over medium heat, whisking often, until it thickens enough to coat the back of a spoon, about 5 to 8 minutes. Season with salt and pepper. Add the Worcestershire sauce if using. Let it cool, then refrigerate for up to 2 days.

On Thanksgiving Day, after your turkey comes out of the oven, skim the fat from the pan drippings using a fat separator or by spooning off the top layer. Pour the defatted drippings (up to 1 cup) into the chilled gravy. Reheat over medium-low heat, whisking until smooth and hot. Taste and adjust salt. Finish with fresh parsley if you like and serve immediately.