Add the butter to a small, well-seasoned cast iron skillet. In this example, I used herbed butter which is delicious, but regular non-salted butter will do just fine.
Melt the butter over medium heat, about 2 minutes. Swirl the butter to evenly coat the pan.
Reduce the heat to low, and carefully crack the eggs into the pan.
For sunny side up
Cook on low, uncovered until the egg whites set, about 2 minutes.
For over easy
After the egg whites have set, add 1 oz water, cover with a lid and cook for 1 minute more. The steam from the water will poach the top of the eggs, so there is no need to turn them over.
For over medium
Follow the same method as over easy, but allow it to cook covered for 1 1/2 minutes.
For serving
Sprinkle with salt and pepper, then use a non-slotted spatula to carefully transfer the cooked eggs to a warm plate. Serve immediately.