The key here is to fry the eggs fast (listen for the sizzle) and baste the yolks with the hot oil until they're opaque.
Light olive oil
Kosher salt to taste
Pour olive oil to depth of 1/3 inch into a small nonstick skillet (about 1 cup oil for a 6-inch skillet). Heat oil over medium-high just until it begins to smoke. Reduce heat to medium. Break 1 egg into a ramekin or small bowl. Holding dish as close to surface as possible, carefully slip egg into oil. (Oil may splatter.) Spoon oil over egg for about 30 seconds or until white is cooked and crispy on edges. Remove egg from oil using a slotted spoon, dabbing with paper towels to absorb oil; transfer egg to a plate. Sprinkle with kosher salt to taste. Repeat with desired number of eggs.