Add flour to a shallow dish. In another shallow dish, lightly beat eggs. In a third shallow dish, combine breadcrumbs, cornmeal, and parmesan. Season with salt and pepper.

Heat ¼-inch to ½-inch of oil in a heavy skillet over medium heat. Dip a tomato slice in flour, then eggs, then the breadcrumb mixture. Add to hot oil. Continue with about a quarter of the tomato slices. Cook until golden brown, 1 to 2 minutes. Flip tomatoes to cook other side until golden brown. Transfer tomatoes to a paper towel–lined plate. Repeat until all of the tomatoes are cooked.

Meanwhile, warm pimento cheese until melted. Stir to incorporate.

Toast bread. Spread equal amounts of warmed pimento cheese on each slice of bread. Top 4 bread slices with a few slices of fried green tomato and 1½ slices of bacon. Top with another piece of bread, cheese side down.