Preheat the oven to 375°F.
In a large Dutch oven (7.5-quart) or a roasting pan, roast the turkey wings, celery, onion, and garlic on the lower oven rack for 2 hours. If the wings and veggies start to darken too much, loosely place a piece of foil on top to prevent burning. Remove from the oven.
Add water to the roasting pot and bring to a boil. (If you used a roasting rack, transfer the mixture to a large stovetop-safe pot.) Reduce the heat and simmer uncovered on low for 1 hour to allow the stock to reduce.
Strain the stock into a bowl with at least a 4-cup capacity. Refrigerate for at least 2 hours or overnight, then remove the layer of fat that forms on top.
In a large sauté pan, melt the butter and whisk in the flour. Cook over medium heat, whisking constantly, for 2 minutes to remove the raw flour taste. Gradually whisk in the defatted turkey stock and cook until the gravy thickens enough to coat the back of a spoon. Stir in the milk, cider vinegar, and salt to taste. Turn off the heat.
