Lay out all the tomato slices and spread 1 tablespoon pimento cheese filling over each slice.
To half of the tomatoes, add a little under 1-½ teaspoons of the remaining shredded cheese.
Top with the remaining tomato slices, filling side down; excess filling can be placed in an airtight contatiner and refrigerated for later use.
Dip the 8 tomato sandwiches into the flour-and-cornmeal mixture and coat well; then dip the tomatoes into the milk-and-egg mixture.
Coat evenly with seasoned bread crumbs, rebreading the edges, if needed, so the cheese doesn’t ooze out later.
Refrigerate for about 10 minutes.
As you chill the tomatoes, line a rimmed sheet pan with paper towels and set a cooling rack on top.
In a large skillet, over medium, heat the oil until it bubbles when you stick the end of a wooden spoon in it.
Working two or three at a time, add the breaded tomato sandwiches to the pan, making sure not to crowd them; they should not touch.
When the tomatoes are browned on one side, flip them using a spatula and fry on the other side; about 2 minutes, until golden brown.
Bring the oil back to temperature between batches.
Transfer to the prepared rack to cool.
Sprinkle with more salt and serve hot, with extra pimento cheese dip or ranch dressing, if desired.