Take the steak out of the fridge 20 minutes before cooking to reach room temperature and season both sides with salt and black pepper.
Heat a heavy skillet over medium-high heat until very hot.
Add 2 tablespoons of butter to the pan and place the steak in the skillet.
Cook the steak for about 4 minutes on one side, then flip it.
Add the remaining 1 tablespoon of butter and tilt the pan, spooning the melted butter over the steak continuously for another 4 minutes for medium-rare.
Remove the steak from the skillet and let it rest for 5 minutes.
In the same skillet, reduce heat to medium and crack the eggs in. Season with salt and pepper.
Cook the eggs sunny side up or to your preference until whites are set but yolks are still runny, about 2-3 minutes.
Serve the butter-basted steak topped with the fried eggs for a rich, indulgent meal.