Begin by peeling the onions and slicing very thinly, use a mandoline slicer if you can. Separate the onion slices and place them in a shallow baking dish and pour the buttermilk over the top.
Press the onions down so they're submerged as much as possible and let them soak on the counter for at least an hour. If necessary, stir them around a bit halfway through the soaking process.
In a bowl, combine the flour, salt, black pepper and cayenne, and set aside.
Pour 1 to 2 quarts canola oil in a pot or Dutch oven. Heat to 190°C, or until a pinch of flour sizzles when sprinkled over the pot.
Using tongs, remove a handful of onions from the buttermilk and immediately dunk into the flour mixture. Coat the onions in the flour mixture, and then tap them on the inside of the bowl to shake off the excess.
Plunge the onions in the hot oil. With a spoon, fiddle with them a bit just to break them up, and watch them. They'll be ready to remove from the oil in no time flat.
When they're golden brown (this should take just a minute or two), remove them from the oil and place on a paper towel-lined plate.
Repeat with the remaining onion slices and serve immediately.