Make this first, whisk together all the ingredients except for the crab in a small bowl, fold in the crab, carefully coating it in the dressing. Try not to break up the crab. Cover and set in refrigerator until ready to make sandwiches.

Make a dredging station. Get three plates out, on the first plate add half of the flour, the second plate add the egg and third plate mix the remaining flour with the cornmeal. Season both the flour plate and the cornmeal mixture with salt and pepper.

In a heavy bottom skillet, heat the oil over medium heat. Oil should be 1/2 inch up the side of the pan.

One by one, place the tomato slices first in the flour, coating evenly. Tap off excess flour then coat evenly with the egg. Finally, coat in the cornmeal mixture and tap off the excess. Fry tomatoes until golden brown, drain on a paper towel-lined plate.