Combine buttermilk, garlic, lemon, rosemary, salt and pepper in a large bowl.
Place turkey in a large resealable container or baggie.
Pour in the buttermilk mixture. Seal the container and place in refrigerator for 8 hours, turning the breast every hour so that each side gets some time in the marinade.
Fire up your Big Easy.
Remove the turkey breast from the marinade, which you will discard.
Pat the breast dry and rub a small amount of olive oil all over the turkey. Transfer to the Big Easy basket
Transfer basket to the Big Easy and cook until the breast measures 165 F as tested in several locations. Use 10 minutes per pound as your starting point. My turkey, a 10 pounder, took 110 minutes.
Remove the basket from the Big Easy. Let cool slightly before removing the breast to a cutting board. Let rest another 15 minutes before carving.