Remove the steak from the refrigerator and let it sit at room temperature for about 15 minutes.
Season both sides of the steak generously with salt and pepper.
Heat a skillet over medium-high heat and add olive oil.
Once the oil is hot, carefully place the steak in the skillet.
Cook for about 4-5 minutes on one side without moving it.
Flip the steak and cook for another 3-4 minutes for medium-rare.
While the steak rests, reduce the heat to medium-low for the eggs.
In the same skillet, crack the eggs carefully and cook until the whites are set.
Season the eggs with salt and pepper to taste.
Plate the steak and eggs, garnishing with fresh rosemary if desired.