At least 4 hours before cooking and up to 24, add the boneless turkey breast to the Dutch oven. Combine the salt with one quart of water and pour over the turkey breast. It should cover the turkey breast completely. Refrigerate until ready to cook.
2 pounds boneless, skin-on turkey breast, ¼ cup kosher salt
When you're ready to cook, heat your oven to 275℉. Remove the turkey breast from the brine and pat it dry with a paper towel. Do not rinse.
Rinse out the Dutch oven and dry it. Add one tablespoon of olive oil or butter and heat over medium-low heat. When hot, add the vegetables, chopped sage, and ground pepper and cook until the veggies are softened and just beginning to brown, about 7 to 10 minutes.
1 tablespoon olive oil or butter, 2 to 3 Yukon gold potatoes, 1 shallot, 2 cloves garlic, 1 tablespoon fresh sage leaves, 1 teaspoon ground black pepper
Turn the heat off, and return the turkey breast to the Dutch oven, skin-side down at first. Pour in the chicken broth and vermouth. The turkey breast won't be completely covered with liquid. Cover the Dutch oven with the lid and transfer it to the oven.
1 cup chicken broth, ½ cup dry white wine or vermouth
Braise for 45 minutes, then remove the lid and flip the turkey breast so it's skin-side up. Cook until the turkey reaches an internal temperature of 165°F (74°C), about 20 to 30 minutes more. You can crisp the skin under the broiler for a few minutes if you like it browner. Remove the turkey from the Dutch oven and let it rest for 10 minutes before slicing.