Slice the tomatoes about ⅓ inch thick. Nice slices. Season lightly with salt and pepper.
Pour the buttermilk into a shallow wide bowl, mix the cornmeal and panko together in another bowl.
Set a wire rack over a cookie sheet.
Dip the tomato slice into the buttermilk coating both sides. Dip into the coating mix. Set on the wire rack. Repeat with all the tomato slices. Once they are dipped, repeat, dip in the buttermilk, and then the coating mix, now they are double-dipped. Set on the wire rack for about 10 minutes to allow the coating to set.
Heat the oil in a large skillet over medium heat. This oil should be about ¼ inch high. When hot, (about 375°F) add the tomatoes, in batches if necessary, don't overcrowd the pan, there should be a lively sizzle. (I find when working with fried foods such as this, it's best to use the clock approach to adding food to the pan, the first piece goes at 12:00 high, then 1:00, etc. so you know where you began and where you should start the turning process.) Once one side has browned, carefully turn and brown the other side. Remove the cook tomatoes to the wire rack to drain. Serve plain or with dipping sauce.