Butterfly the turkey breasts by slicing them horizontally almost all the way through, then open them up like a book. Pound them to an even 1/4-inch thickness.
Season the inside of the flattened turkey breasts with salt and pepper. In a skillet, cook bacon until crisp, then remove bacon and crumble. Sauté mushrooms and onion in bacon drippings until softened, add minced garlic and cook for 1 minute more. Stir in kale/spinach, thyme, and sage; cook until greens are wilted.
Spread the cooked vegetable and bacon mixture evenly over the seasoned turkey breasts, leaving a small border.
Tightly roll up the turkey breasts from the wide end, securing with kitchen twine or toothpicks.
Preheat your air fryer to 370°F (188°C).
Place the rolled turkey breasts in the air fryer basket, ensuring not to overcrowd. Air fry for 25-30 minutes, or until the internal temperature reaches 165°F (74°C). Let rest for 5-10 minutes before slicing.