Pull steaks from the refrigerator for 30 minutes prior to cooking. Brush olive oil lightly over all sides. Then, season generously with salt and pepper. Allow to rest at room temperature for the rest of the 30 minutes.
Meanwhile, fire up the grill over high heat.
Right before cooking, sprinkle fresh thyme on the steaks. Place the filets on the grill over direct heat. Allow to sear for 4-5 minutes until a rich, golden-brown crust forms. Then, flip the filets over to the other side to sear for another 4-5 minutes.
Using tongs, hold the filets on their sides, rotating them occasionally to sear all sides of the filets.
Check the internal temperature with a steak thermometer. For medium-rare, the steaks should come to about 130 degrees. If they need a little more time to cook, lower the heat on the grill, close the lid, and allow them to cook for a couple more minutes.
Remove filets from the grill. Tent them loosely with foil, allowing them to rest for 5-10 minutes.
Just before serving, add 1 tbsp of butter to the top of each filet. Enjoy!