Preheat oven to 475 degrees F.
Liberally season both sides of the steaks with salt and pepper and set aside to rest.
Over MED-HIGH heat, heat a large cast iron skillet (or oven proof pan) and add olive oil and butter.
Carefully place both steaks in the skillet, leaving room between the two. Once the steaks are in the pan, do NOT move them. Cook for 4 minutes, turn steaks over and cook another 4 minutes. If you try to flip the steaks and they are sticking to the pan, it means the steaks aren't ready to flip yet. Give them another 20-30 seconds and try again.
Remove pan from the heat, add garlic and thyme and slide pan carefully into the oven.
Bake about 5 minutes, then check doneness with a meat thermometer.
Once steak reaches desired doneness (about 135-140 for medium rare), remove from the oven.
Spoon pan juices over the top of the steak, add a pat or two of the compound butter, and let rest for 5-10 minutes.
Serve with an additional pat of compound butter, caramelized onions, and additional fresh thyme if desired.