Season the steaks with a sufficient amount of salt and pepper.

Place a pan over medium-high heat and add 1 tablespoon olive oil. Once heated, add the steaks to the skillet and cook for 4-5 minutes each side for medium-rare, or until desired doneness. Allow to rest after removing from the skillet.

In the same skillet, turn the heat down to medium. Cook until the butter, garlic, and thyme have melted and become aromatic.

Crack the eggs into the skillet, taking care not to break the yolks. Season with salt and pepper. Cook until the whites are set but the yolks are still runny, which should take around 2-3 minutes.

Top the steaks with eggs and spread some garlic-thyme butter over them.