Combine softened butter with thyme leaves remaining butter ingredients.
Scoop out onto the plastic wrap and carefully roll one side of plastic wrap, creating a cylindrical shape out of the butter. Twist the ends of plastic and fold under the body of the sealed butter.
Place into the refrigerator for at least 2 hours before using. Butter mixture will last for a week if stored covered in the fridge.
Preheat grill for high heat. Brush olive oil onto the exposed areas of the filet. Season both sides of with salt and black pepper.
Place steaks on the grill and cook 5 minutes per side, depending on the thickness of the cut and preferred doneness. I recommend an internal temperature between 135-140 degrees F--medium-rare or medium. Reduce heat if needed. Once cooked to your liking, remove steaks from the grill and let them rest for 5 minutes. Top with 1 inch thick slices of compound butter and serve with your favorite sides.
Please note that you can swap out the thyme for another fresh herb such as Italian parsley, basil, oregano, or rosemary. You can also omit the black pepper entirely from the butter.