Skillet-cooking is among the easiest ways to prepare okra and is guaranteed to please Southerners and neophytes alike.
Heat oil in a cast-iron or heavy skillet until a frying thermometer registers 375 degrees.
Wash okra under cold water; pat dry with a paper towel. Trim stem ends; cut each pod crosswise into 3/4-inch pieces.
Whisk together the eggs and milk in a medium bowl; set aside. Place cornmeal, flour, salt, black pepper, and cayenne in another bowl; whisk to combine.
Add okra to egg mixture; stir until evenly coated. Add cornmeal mixture; toss with hands or a spatula until evenly coated.
Fry okra in batches until golden brown, turning as necessary, 1 to 2 minutes per batch. Drain on paper towels, and season with salt. Serve warm with hot-pepper sauce, if desired.