Take the beef fillets out of the refrigerator about 30 minutes before cooking to bring them to room temperature. Clean steak, remove fat and cut 1 cm thick slices, then wash and drain.
Place beef pieces flat on tray, sprinkle with salt, black pepper and lemon pepper. Turn each piece and sprinkle on the other side as well.
Heat oil & butter in a large non-stick pan. Saute garlic in oil & butter until it's golden brown.
Add fillets to the pan. For medium-rare, cook for about 3-4 minutes on one side without moving them.
Flip the fillets, add thyme (if using). Cook for another 3-4 minutes, adjusting the time based on your desired doneness (see notes below).
Once cooked to your liking, remove the fillets from the pan and let them rest for 5 minutes. This allows the juices to redistribute.
Serve hot with your favorite sides, like mashed potatoes or a green salad.