Heat a large cast iron skillet to high heat. Add the olive oil and butter and let it heat up for a minute before adding the steak.
Place the seasoned steak in the skillet.
Cook on each side for 4 minutes or until the outside is browned. Reduce heat to medium-high heat. Cook the steaks to the desired doneness. Mine took about 8 minutes flipping 3 times to get a medium. Once the steak is done, move it aside on the skillet to make room for the eggs.
Keeping the heat at medium heat, crack the eggs slowly into the skillet. Cover with a tight lid and cook until the whites are completely set, but the yolks are still runny. This will take about 2 to 2 ½ minutes. Watch it closely, and don’t remove the lid until after 2 minutes. Remember, no flipping if you want your eggs sunny side up. Season the eggs with salt and pepper.
Slice up your steak and serve with your eggs and your choice of side.