I started with this recipe as a reference:
and tweaked it based on what we had on hand. I cooked them in a deep fryer using peanut oil.
2 smallish (about 3" diameter) white onions, cut into 1/2" slices and separated into rings
1 1/4 cups self-rising flour
1 tsp salt, plus additional to taste
1 cup milk
1/2 to 3/4 cup breadcrumbs
Heat the oil to 365 degrees. Stir the flour and salt together, and use it to coat the onion slices - my preferred method is to toss everything into a plastic bag and shake it around. Remove the onion slices to a plate. Put the flour/salt mixture into a mixing bowl, and whisk in the milk and the egg. Dip the onion slices in the batter - I did 3 or 4 at a time - and set them on a wire rack to let the excess drip off. Put the breadcrumbs in a bowl, and dredge each onion ring through until coated. They're ready for the fryer now.
I think that I'm not officially supposed to do this, but I lower the fry basket into the oil and drop the onion rings in a couple at a time. This seems to keep them from becoming one with the basket or each other as they're prone to do when I put them in before the basket goes into the oil. Cook the onion rings until they're golden brown; this batch took about 3.5 minutes. Drain them on a paper towel, shake a little salt over the top, get out your bowl of aioli, and go to town.