Preheat the oven to 200°F and get a large baking sheet ready for the finished fried green tomatoes to keep warm.
In a 10-inch cast iron skillet, heat 1 to 1½ cups of peanut oil over medium-high heat. The oil is ready when there are bubbles around the end of a wooden spoon. Make sure the oil level is shallow, since you don't want to submerge the slices. If the oil is bubbling too much, or smoking, turn the temperature down.
Using a metal flipper, carefully lower 4 tomato slices into the hot oil. You don't want to overcrowd the skillet, as it will lower the temperature of the oil. Turn the heat down to medium.
Cook the tomatoes for 2 to 3 minutes per side, until nicely browned. Flip the slices using metal tongs, being careful not to splatter oil.
Once the tomatoes have nicely browned, use the metal tongs to move them to a baking tray. Optional, while they are still warm, sprinkle salt on both sides of the tomato slices.
Keep the batches of fried green tomatoes warm by placing them on a cookie sheet in a 200°F oven.
Serve the fried green tomatoes hot or warm. You can serve them plain, with a spicy dipping sauce, lemon wedges, or a sweet onion relish. Fried green tomatoes are also used in grilled sandwiches, and are part of the traditional Southern vegetable plate. They also taste great with a poached egg in a breakfast sandwich.