Season both sides of the filet generously with salt and pepper and fresh rosemary. Rub with a little olive oil and let rest for 30-45 minutes before cooking, this is to bring the steak to room temperature and ensure your cooking times are more accurate.
Preheat the grill to high heat for 10-15 minutes and clean the grates well. Keep the lid closed and let the internal temp get up to around 500°F. Once hot, reduce heat to medium-high heat (shoot for a constant temp of around 400-450°F).
Place the filets face down and sear undisturbed for 5 minutes with the cover down. Flip the filets and sear for an additional 5 minutes with the cover down. This is ideal for medium-rare.
For rare, sear for 4 minutes a side. Medium rare, 5 minutes. Medium, 6-7 minutes. Medium well, 8+ minutes. Depending on the size of the steak, the more or less time it will take. This recipe is ideal for an 8-10 ounce portion, roughly 2 inches thick. Remember, the steak will continue to cook after it's been removed from the heat. Test the temperature with a digital thermometer. Steaks should be removed from the heat 5-7 degrees below the final serving temp.
Remove filets from the grill and let rest for 7-10 minutes before serving. This is important to bring your steak to its final serving temperature. Top with a slice of garlic and herb butter and serve.