Rub both sides of the steaks with the split garlic halves. Coat both sides of the steaks with a generous sprinkle of pepper. Coat each steak with ½ tablespoon oil and press on ½ tablespoon of the oregano. Wrap the steaks in plastic wrap and let them sit at room temperature for 1 hour (see tips).
Preheat a large skillet to medium heat. Add the butter and the remaining 1 tablespoon olive oil. Remove the steaks from the plastic wrap and sprinkle each with 1 teaspoon salt. Add the steaks to the hot pan and cook 2 minutes on the first side, or until they are seared a nice, deep brown. Turn the steaks over and add the lemon to the pan, cut-side-down. Turn heat to medium low and cook for 2½ minutes more, or until the steaks become browned on the bottom. Your steaks will be medium rare at this point. Add a little more cooking time if you prefer your steak more well done.
Remove the steaks to the cutting board and let them rest 5 to 10 minutes before serving. Squeeze the pan-fried lemon over the two steaks. Serve immediately.
Notes
To make this recipe dairy free, leave out the butter and use all olive oil instead.
Cooking a steak at room temperature will allow for it to cook more evenly and quickly.
You'll get a better result in pan-frying your steaks if you avoid using a nonstick skillet. The steaks will brown more nicely and hold a better texture if you opt for a stainless steel or cast-iron skillet.
MAKE-AHEAD TIP: Wrap the steaks in plastic wrap and let them marinate in the refrigerator for several hours or up to 1 day. Remove the steaks from the refrigerator and let them sit at room temperature for 1 hour before serving.
USING THE GRILL INSTEAD: Preheat your grill to medium and grill the steaks 3 to 4 minutes per side for medium-rare. Grill the lemon cut-side-down.