Heat to 365°F in a large skillet:
While the oil heats, wash, dry, trim off the stems, and slice into ½-inch pieces:
In a medium bowl, combine:
Set aside. Whisk together in a second medium bowl:
Toss the okra in the milk mixture, then in the cornmeal mixture. Add the okra to the hot oil in batches and fry, stirring occasionally, until browned, 4 to 6 minutes. Do not crowd the skillet and keep an eye on the temperature of the oil, adjusting the heat of the burner as needed. Remove the okra with a slotted spoon and drain on paper towels. Serve immediately.