Season both sides of the filet generously with salt and pepper. Let rest for 30 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 and clean the grates well. Keep the lid closed and let the internal temp get up to around 500°F.
Place the filets face down and sear undisturbed for 5 minutes with the cover up. Flip the filets and sear for an additional 5 minutes. 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. Note: If your steak still needs more time, lower the heat to medium and put the cover down. This will take advantage of the ambient heat to finish the steak. Remember, the steak will continue to cook after it's been removed from the heat. More notes below.
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.
As the steaks are resting, drizzle/brush the oil (about 2 teaspoons per side) on both sides of each slice of bread. Grill for 1-2 minutes per side over medium heat or until golden and toasted.
Thinly slice tenderloin into 1/4-inch thick strips. Layer over bread slices and season with sea salt. Top with a few spoonfuls of chimichurri. Eat with a fork and knife or with your hands. See notes on serving size/quantities.