science

For actual cooking, chop off the root part (it holds all the layers together), then perform two cuts to chop the onion in four equal pieces. Then press each quarter with your finger and it will separate into individual layers thin enough to fry in a pan.

You can even do it with two half-onions, but you'll squish some layers when separating them, or you'll spend too much time carefully separating them with a knife or a spoon.