Instructions:

1. Begin by generously seasoning the steaks with salt and pepper on both sides.
2. Heat a skillet over medium-high heat and add 1 tablespoon of olive oil. Once the oil is hot, carefully place the steaks into the skillet. Cook for about 4-5 minutes on each side for medium-rare, or adjust based on your preferred doneness. Remove the steaks from the skillet and allow them to rest.
3. Reduce the heat to medium and use the same skillet. Add the unsalted butter, minced garlic, and fresh thyme leaves. Cook until the butter has melted and the mixture becomes fragrant.
4. Gently crack the eggs into the skillet, being cautious not to break the yolks. Season the eggs with salt and pepper to your taste. Cook until the egg whites are fully set while ensuring the yolks remain slightly runny, approximately 2-3 minutes.
5. To serve, place the rested steaks on plates and top each with an egg. Spoon some of the garlic-thyme butter over the steaks and eggs.