If you are making the broth, preheat the oven to 425°F. Coat the turkey wings in the vegetable oil and salt well. Roast in a cast iron frying pan or other oven-proof pan until nicely browned, from 45 minutes to an hour. Put the roasted wings in a pot with all the other ingredients for the broth and bring to a simmer. Simmer gently until the meat wants to fall off the bones. This will take about 90 minutes with a domesticated turkey, longer for wild. You can pick off the meat and eat it later, or you can chop it up and put some in the gravy, too.
Once you have the broth made, take the turkey breast out and salt it well. Let it sit on a cutting board for 30 minutes or so to come to room temperature.
Bring the broth to a simmer and drop the turkey breast in. The turkey should be submerged by the broth. If it is not, add water or chicken stock. Once the turkey is in the broth, move the pot to your weakest burner and turn the heat to its lowest setting. Cover the pot and let it steep in the hot broth for at least 30 minutes, and up to 1 hour if you are using a full half breast. Remember to never let the water simmer! You are looking for a target temperature of 155°F to 165°F. So long as you are in that ballpark, you will not overcook the turkey.
Make the gravy while the turkey is poaching. Heat the butter in a small pot over medium-high heat. When it's hot, add the flour and mix well. Cook this, stirring often, until it smells nutty and turns milk-chocolate brown, about 10 minutes. Stir in the sherry. The mixture will seize up, so slowly stir in 1 cup of the hot broth until the gravy has the consistency of melted ice cream. Add salt, black pepper and Worcestershire sauce to taste. Turn the heat to low and stir from time to time. If it gets too thick, add a little more broth.
To check if the turkey has cooked all the way through, either test it with a meat thermometer -- you want it to read 150°F -- or slice the thickest part and look: You want a blush of pink in the meat. Slice and serve with mashed potatoes and a vegetable of your choice. Ladle over lots of gravy!