Break the eggs into a shallow bowl and season with salt and pepper. Combine the cornmeal and flour in a second shallow bowl and season with salt and pepper.
Line a plate with paper towels and set near the cooktop.
Heat the oil in a large skillet over medium heat. Working a few at a time, season the tomato slices lightly on both sides with salt and pepper. Dip the tomato slices into the egg mixture and shake off the excess. Place the dipped slices in the cornmeal mixture, sprinkle breading over, and press to adhere. Turn over and repeat to coat on both sides. Gently shake off the excess and place without crowding in the heated skillet.
Fry the tomato slices until they are golden on one side, about 3 minutes, then gently turn them with an offset spatula or metal turner and continue cooking until golden on the other side. Remove them to the prepared plate. Season with salt and pepper and serve immediately.