Place a cast iron skillet over medium-high heat for about 3 minutes until piping hot.

Season both sides of the ribeye liberally with coarse sea salt.

Add 1 tbsp butter; when foaming, sear the steak 90 seconds untouched, flip, sear 1 more minute, then transfer to a plate to rest.

Reduce heat to medium-low and add the remaining 1 tbsp butter to the pan drippings.

Crack the eggs into the butter and cook slowly until the whites are set but the yolks stay runny.

Slide the eggs next to the steak and spoon the extra butter drippings over the top.