What's a Spanish fried egg? It's an egg fried very quickly in very, very hot olive oil. What you get is a crispy, delicate white that crunches then practically melts in your mouth. The yolk is just set, but still runny enough to melt into your toast.
Soaking onions in ice water for 10 or 15 minutes mellows out the flavor to take that sharp edge, and accompanying aftertaste, out of the picture. It's a trick restaurants use, and you can achieve the same results, too.