Season filets with salt and pepper and lightly brush with olive oil. Heat grill to high. Place steaks on grill, reduce heat to medium. Cover and cook for 5 minutes. Flip and cook for an additional 5 minutes. Reduce to low, top with one tomato slice, one basil leaf, one slice mozzarella, another basil leaf, and another slice of tomato. Close the cover and grill for another 3-5 minutes or to desired doneness.

Remove to a platter, let rest for at least 5 minutes, drizzle with olive oil and balsamic vinegar before serving.