Slice the tomatoes into ½-inch thick slices and set aside.
Set out three shallow bowls. In the first bowl, whisk together ½ cup of the flour, ¼ teaspoon of the salt, and ⅛ teaspoon of the black pepper. In the second bowl, whisk together the egg and buttermilk. In the third bowl, stir together the cornmeal, the remaining ¼ cup flour, the remaining salt, and the remaining pepper.
Working with one slice at a time, dredge the tomato slices in the flour mixture. Dip them into the egg mixture, letting the excess drip off, then coat in the cornmeal mixture. Place the coated slices on a wire rack set over a baking sheet and refrigerate for 15-30 minutes to help the coating adhere.
Pour oil into a large cast iron skillet or Dutch oven to a depth of about 1 inch. Heat the oil over medium heat to about 350°F-375°F.
Working in batches and without crowding the pan, carefully add the green tomato slices to the hot oil. Fry until golden brown and crisp on the first side, about 3 minutes, then gently flip and cook until golden on the second side.
Transfer the fried green tomatoes to a paper towel-lined plate, season lightly with additional salt and pepper if desired, and serve immediately. If you like, serve them with ranch dressing or a classic Southern remoulade sauce for dipping.