Place the turkey breast in a large, deep stock pot and cover it with water so that the water level sits about 3 inches above the meat. Mark this water level, then remove the turkey breast from the pot. This is the amount of oil you will need to fry your turkey breast. Make sure your pot is large enough that the oil (and later, the turkey) will come no more than halfway up the sides to prevent spills.
Pat the turkey breast dry thoroughly with paper towels. Season it generously with kosher salt and fresh ground black pepper all over. Leave the seasoned breast to air dry at room temperature for 1 hour, or refrigerate it uncovered for 1 to 24 hours for even better flavor and skin texture.
Dry out the pot used to measure the oil. Pour in the previously measured amount of canola or peanut oil. Heat the oil over medium-high heat until it registers 350°F on a deep-frying thermometer. This step is crucial for safe and crispy results—I always double check the temperature before moving on.
With care and wearing protective gear to avoid splatters, slowly lower the seasoned and air-dried turkey breast (from Step 2) into the hot oil (from Step 3). Fry the turkey, turning it once halfway through, until the skin is golden brown and the internal temperature at the thickest part reaches 165°F. Maintain the oil temperature at 350°F during cooking. Fry time is about 3–4 minutes per pound, plus 5 minutes—a 2½–3 lb breast typically takes 15–20 minutes.
Once cooked, remove the turkey breast from the oil and let it rest for 5 minutes before slicing into ½-inch thick slices. I like to let it rest just a little longer if possible to keep the meat juicy and flavorful.