Heat a nonstick, or well-seasoned cast-iron, skillet slowly over medium heat (you don’t want it too hot). Add 2 tablespoons of butter to the pan to melt. Carefully crack 4 eggs into the pan, and gently work a spatula around the edges of the eggs to prevent the whites from sticking to the bottom.
Cook at a gentle simmer until the egg whites turn a solid opaque color (if the outsides cook faster than the insides, cover the pan with a lid to steam the eggs for a minute). The yolks should stay soft. To remove the eggs, tilt your pan and slide them gently onto your serving plate. Season with sea salt and fresh-ground pepper to taste.