Heat oil in a large Dutch oven or heavy-bottomed pot over high heat. Add the chicken wing pieces in a single layer and cook until deeply browned on all sides. Remove the wings to a plate and set aside.
Add the onion, carrot, and celery to the pot. Cook, stirring occasionally, until the vegetables are well-browned, about 8-10 minutes. Getting a dark color on the onions is key for a rich flavor.
Return the chicken wings to the pot. Add the thyme, sage, and whole peppercorns. Pour in the red wine to deglaze, scraping up any browned bits from the bottom of the pot with a wooden spoon.
Add the 6 cups of water and bring to a boil. Once boiling, reduce the heat to low, cover the pot, and let it simmer for 1 hour. After an hour, turn off the heat and let the stock rest, still covered, for 30 minutes.
Strain the stock through a colander or coarse-mesh sieve into a clean saucepan, discarding the solids. Bring the strained stock to a simmer over medium-high heat and cook until it has reduced to about 3 cups, which takes about 30 minutes. This concentrates the flavor.
In a separate medium saucepan, melt the butter over medium-low heat. Whisk in the flour to form a paste, or roux. Cook, whisking constantly, for 3-5 minutes until the roux is a light golden brown and smells nutty.
Take 2 cups of your warm, reduced stock. Whisk the miso paste, Worcestershire sauce, brown sugar, and ground black pepper into the stock until smooth.
While whisking the roux constantly, slowly pour the seasoned stock into the saucepan. Continue whisking to prevent lumps.
Increase the heat to medium and bring the gravy to a gentle simmer. Cook, whisking often, for about 5 minutes, until the gravy has thickened and coats the back of a spoon. Taste and season with salt as needed. For an extra-smooth finish, strain the gravy through a fine-mesh sieve before serving or storing.