Prepare a baking sheet by lining it with paper towels.
Peel onions and slice then 1/2 – 3/4 inch thick. Separate into rings.
Add 1 tsp. of salt and 1 tsp. of pepper to the buttermilk. Drop the onion rings into the buttermilk mixture and let set for half an hour (can sit as long as a few hours). Mix the rice flour and cornmeal with 1 1/2 tsps. of salt and 1 tsp. of pepper.
Heat the vegetable oil in a large pot or Dutch oven to 275 degrees F. If you have a candy thermometer this really helpful for maintaining the correct frying temperature – clip it on the side of the pot.
Working in small batches, take some onion rings out of the buttermilk and dredge in the flour mixture the carefully drop into the hot oil. Make sure you do not over crowd. Fry for about 2 minutes or until golden brown turning once during frying. Take onion rings out of oil and put on prepared baking sheet and sprinkle with some additional salt. Keep them warm in the oven while you fry the rest of the onion rings. For best results keep the oil temperature between 250 and 300 degrees F. If it drops below 250 degrees F then wait until it comes back up to temperature before adding the next batch of onion rings.
The onion rings will stay nice and crisp in the oven for at least 30 minutes.