Préparations
Season the steaks generously with salt and pepper.
Heat a skillet over medium-high heat and add 1 tablespoon olive oil. Once hot, add the steaks to the skillet and cook for about 4-5 minutes on each side for medium-rare, or until desired doneness. Remove from skillet and let rest.
In the same skillet, reduce heat to medium. Add butter, garlic, and thyme, cooking until butter melts and is fragrant.

Crack the eggs into the skillet, being careful not to break the yolks. Season with salt and pepper. Cook until the whites are set but yolks are still runny, about 2-3 minutes.
Serve the steaks with eggs on top, spooning some of the garlic-thyme butter over them.