Put the onions in a large bowl and add enough buttermilk to cover. Cover the bowl and refrigerate for at least 1 hour and up to 12 hours. In a cake pan or pie plate, combine the flour, cornmeal, and salt.
Position a rack in the center of the oven and heat the oven to 200°F. Have ready a large rimmed baking sheet fitted with a rack. Line a plate with a few layers of paper towels.
Pour 1 inch of oil into a 5-quart Dutch oven or other heavy-duty pot and clip a deep-fry thermometer to the side of the pot. Heat over medium heat until the thermometer registers 350°F. Working in batches of 4 or 5, remove the rings from the buttermilk, letting any excess drip off, then dredge in the flour mixture, knocking off the excess.
Carefully lower the rings into the oil and fry until lightly browned on one side, about 2 minutes. Using tongs, gently turn the rings over and continue to fry, adjusting the heat as necessary to maintain a steady temperature, until golden-brown all over, about 2 minutes. Transfer to the paper towels to drain. Sprinkle generously with kosher salt, then transfer to the rack on the baking sheet and keep warm in the oven.
Continue to fry the onions in batches, letting the oil return to 350°F between batches and replacing the paper towels on the plate as needed. Serve with ketchup, if you like.