Let the steak come to room temperature before cooking. Preheat a cast iron skillet over medium heat on the stove and add the oil to the pan.
Sprinkle salt and pepper on the steak or any other desired seasoning. Bring the heat under the pan to high.
After one to two minutes of heating, place the steak in the hot pan.
Let it cook for about 5 minutes (rare) to 7 minutes (medium) on the first side, then flip. It should only take three to four minutes on the opposite side to reach medium rare. Let it continue cooking for a higher level of doneness, using a meat thermometer to check it often.
Remove the steak from the pan and let it rest on a plate for at least 10 minutes.
Prepare your eggs as desired in a non-stick pan or pot of water, depending on the method.