Begin by peeling the outer layers of the onion. Slice the onions very thinly into rings (ideally using a mandolin slicer if available). Separate the onion rings and place them in a gallon size bag. Pour the buttermilk over the top of the onions. Press the onions down so they're submerged as much as possible, remove air from bag and seal. Let them soak in the fridge for at least an hour.
In another gallon size bag, combine the flour, salt, black pepper and cayenne, and set aside.
Pour 1 to 2 quarts of vegetable or canola oil in a large pot. Heat the oil to 375 degrees or until a pinch of flour sizzles when sprinkled over the oil.
Line a baking sheet with parchment paper and place a wire rack on top. Set aside.
Remove a handful of onions from the buttermilk and immediately toss into the flour mixture. Coat the onions in the flour mixture, and then gently shake off the excess.
Gently place the onions in the hot oil (using tongs to prevent any burns). Using the same tongs, gently move the onions around in the pot to prevent any sticking. Watch the onions closely as the cook quickly.
Once they are golden brown, remove them from the oil and place on the wire rack. Season lightly with salt. Place baking sheet in oven set on warm.
Repeat with the remaining onion slices and serve hot.