Slice tomatoes into ½-inch thick slices.
Set out three shallow bowls. In the first, whisk together flour, salt, and pepper. In the second bowl, whisk together the egg and buttermilk. Place the cornmeal in the third.
One at a time, dip the tomato slices in the flour mixture, then into the egg mixture (shake off the excess), and then dredge in cornmeal. Place on a wire rack on top of a baking sheet and refrigerate for 15-30 minutes.
Pour oil in a cast iron skillet or Dutch oven to a depth of about 1 inch. Heat oil over medium heat to a temperature of about 350°F. Without crowding the skillet, fry tomatoes in batches until golden brown on one side (about 3 minutes). Gently turn, and continue cooking until golden on the other side.
Remove to a paper towel-lined tray, season with salt and pepper, and serve immediately.