Special equipment: a deep-frying thermometer; an instant-read thermometer
One hour before frying, place the turkey breast on a baking sheet, sprinkle liberally with salt and pepper, and let sit at room temperature.
To figure out how much oil you will need for frying, put the breast in a large pot and cover with water by 3 inches; the pot should be large enough that the water comes no more than halfway up the sides. Remove the breast and check the water level -- that is how much oil you will need.
Dry the pot and add the oil. Heat to 350 degrees F on a deep-frying thermometer.
Pat the breast dry with paper towels. Using heat-resistant gloves (to protect yourself from burns), SLOWLY and CAREFULLY lower it into the hot oil.
Fry until golden brown and the internal temperature reaches 160 degrees F on an instant-read thermometer, 15 to 20 minutes. Remove to a paper towel-lined baking sheet and season with a bit more salt. Let rest for 5 minutes before slicing.