Make the turkey: Place 3 tablespoons unsalted butter in a medium bowl and let sit at room temperature until softened. Prepare the following, adding them to the butter: 1 tablespoon fresh thyme leaves, 1 tablespoon chopped fresh rosemary loaves, 1 tablespoon chopped fresh sage leaves, 1 teaspoon finely grated lemon zest, and 2 minced garlic cloves. Add 1 teaspoon of the kosher salt and 1/2 teaspoon of the ground black pepper, and stir and smash everything together into a paste.
Pat the turkey breast dry with paper towels. Loosen the skin of the turkey breast. Spread the butter mixture in an even layer under the skin. Season the outside of the turkey breast with the remaining 1 teaspoon kosher salt and 1/2 teaspoon ground black pepper.
Line the bottom tray of an air fryer with a sheet of aluminum foil. Heat the air fryer to 350ºF and set the cook time for 55 minutes. Place turkey skin-side down into the bottom rack of the air fryer when indicated. Cook for 20 minutes. Flip the turkey so it is skin-side up and continue to cook until an instant-read thermometer inserted in the center registers at least 160ºF, 25 to 30 minutes more. Transfer the turkey to a clean cutting board and let rest at least 10 minutes. Meanwhile, make the gravy.
Make the gravy: Melt 4 tablespoons unsalted butter in a medium saucepan over medium heat. Whisk in 1/4 cup flour and cook for 2 to 3 minutes. While whisking continuously, slowly pour in 2 1/2 cups turkey or chicken stock, and simmer until the gravy is thickened, about 3 minutes. Taste and season with salt and pepper as needed. Carve the turkey and serve with the gravy.
