Cut onions crosswise into 1 inch thick slices. Separate slices into individual rings and remove thin papery membrane from inside of each ring.
In medium stockpot over medium heat or tabletop deep fryer, heat oil to 375. Pour buttermilk into large baking dish; season with salt and pepper. Divide flour between 2 separate dishes; season each with salt and black pepper and 1/4 tsp cayenne pepper.
Working in batches, dredge onion rings in first flour dish;tap off excess. Dip rings in buttermilk, allow excess to drip off, then dredge in second flour dish, making sure to coat rings evenly. Tap off excess and transfer coated rings to hot oil. Fry, turning once or twice, until golden brown (about 4 minutes). Remove rings with mesh skimmer and drain on paper towel lined baking sheet. Season with salt. Repeat until all onion slices have been cooked. Serve hot.