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Start by making sure the turkey breast will fit into your air fryer. Trim the rib bones with a pair of sharp poultry scissors if necessary to make sure the turkey will fit nicely and not sit higher than the top of the basket.
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Combine the butter, chopped fresh herbs, salt and freshly ground black pepper in a small bowl. Gently slide your fingers underneath the skin of the turkey to loosen the skin away from both sides of the turkey breast. Place a third of the herb butter under the skin, massaging it over the turkey breast. Repeat with the other side. Melt the remaining herb butter in a small saucepan (or in the microwave) and brush it all over the skin of the turkey breast, or flatten the butter with your hands and let it rest on top of the turkey.
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Pre-heat the air fryer to 350°F.
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Place the turkey breast skin-side up in the air fryer basket. Air-fry for 20 minutes at 350ºF. Turn the turkey breast over so that it is now skin-side down. Use a turkey baster to suck up some of the juices from the bottom drawer and baste the turkey breast with the drippings. Air-fry for another 20 minutes.
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While the turkey is air-frying, make the gravy on the stovetop if you choose to do so. Pre-heat a 2-quart saucepan over medium heat. Add the butter and let it melt. Add the flour and whisk the butter and flour together, cooking for about 2 minutes. Add the brandy or white wine and let it bubble and thicken. Then, whisk in the stock, continuing to whisk until the mixture comes to a boil and thickens. Season with salt, freshly ground black pepper and the Worcestershire sauce and then set the gravy aside.
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Turn the turkey breast back over so that it is once again skin-side up. Baste again with the juices from the bottom of the air fryer drawer and air-fry for another 10 minutes, until the skin is crispy and the turkey reaches an internal temperature of 165°F on an instant read thermometer.
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Place the turkey breast on cutting board and let it rest for at least 15 minutes before carving. While the turkey rests, pour the juices from the bottom of the air fryer into a measuring cup or fat separator. Let the juices sit for 10 minutes and ladle or pour off the grease that rises to the surface. Strain the drippings and either add them to the gravy or just pour the juices over the sliced turkey breast.