Combine the butter, cheese, and thyme in a bowl and season with salt and pepper, to taste. Cover the bowl and refrigerate for 30 minutes.
Brush the steaks with some canola oil, then season them with salt and cracked black pepper. Grill until the meat chars on both sides and is cooked to a medium-rare doneness. Transfer the steaks to a platter, top them with some of the butter and let them rest for 5 minutes before serving.