Add the egg halves. Fry them until golden brown, about 3 minutes per side. If the butter browns too much, slightly reduce the heat and keep cooking.
Season the eggs with salt and pepper and serve.
Keep leftovers in the fridge, in an airtight container, for up to 3 days (unless the eggs you used have already spent some time in the fridge).
Video
Notes
You want the yolks of the eggs you use in this recipe to be fully cooked. So if you use my tutorial for how to boil eggs, you should keep them in the water for the full 12 minutes so that the yolks are fully cooked.