Whisk together the remaining 1½ cups flour, the cornmeal, salt, black pepper and cayenne pepper in a second large shallow dish.
In a medium bowl, whisk together the egg, buttermilk, baking powder and baking soda (the mixture may bubble and foam).
Working with several slices at a time, coat the tomatoes in the flour and shake any excess flour from each piece. Using tongs, dip the tomatoes into the buttermilk mixture, turning to coat and allowing the excess to drip off. Coat the tomato slices with the seasoned flour-cornmeal mixture, shaking off any excess. Place the tomatoes on a wire rack set over a rimmed baking sheet. Repeat with remaining tomato slices.
Pour enough oil into a 12-inch cast iron skillet to measure ⅓-inch in depth. Heat the oil over high heat until it reaches 350 degrees F, 3 to 4 minutes. Gently lay a single layer of tomato slices in the oil (be sure not to crowd the pan) and turn the heat down to medium. Fry until the tomatoes are a deep, golden brown on the first side, 2 to 2½ minutes, adjusting the heat as necessary to maintain the oil at a temperature of 350 degrees. Gently turn the tomato slices over with tongs and fry until the second side is a deep, golden brown, 2 to 2½ minutes longer. Transfer the fried tomatoes to a rimmed baking sheet lined with paper towels and cool for 1 to 2 minutes. Repeat with the remaining slices, adjusting the heat as necessary to maintain the oil at a temperature of 350 degrees. Serve immediately.