Rinse the tomatoes with cool water and pat them dry with paper towels. Slice them into 3/8" thick slices. (That's between 1/4 and 1/2" thick). Do not pat the cut surfaces of the tomato dry with paper towels.
Pour enough oil into a cast iron or stainless steel skillet to reach a depth of 1/4" to 1/2" . The oil gets too hot for some nonstick skillets. Heat the oil over medium heat until very hot but not smoking. You will know it is ready when you sprinkle a few grains of cornmeal in it and it immediately sizzles. You can also use a candy thermometer if the oil is deep enough. I absolutely love using a digital, no contact infrared thermometer. You just point it at the oil and it reads the temp. Amazing. You want the temperature to be between 360 and 375 degrees. Keep a close watch on the oil while dredging the tomatoes.
Gather 3 small plates or shallow bowls. I like to use paper plates for the dry mixtures for easy clean up. In one plate, combine the flour and 1/2 teaspoon of the salt. In the second plate, whisk together the milk and egg with a fork. In the third plate, the cornmeal, breadcrumbs, pepper, the remaining 1/2 teaspoon salt and pepper.
Working with 2 or 3 tomato slices at a time, press the tomato slice into the flour, coating both sides. If the flour doesn't stick to the edge of the tomato, run the edges through the egg/milk mixture, then back in the flour. Dip the flour coated slice into the egg/milk mixture, then gently press it into the cornmeal mixture.
I use tongs to lower the tomatoes, 3 at a time, into the hot oil and to remove them. Cook them about 1 minute on each side or until golden brown on both sides. If the tomato slices do not sizzle, the oil is probably not hot enough and will absorb too much oil and take too long to get brown on the outside. This also causes the tomatoes to overcook and become mushy. Drain the tomatoes on paper towels.