Season filets with salt and pepper and lightly brush with olive oil.
Heat grill to high. Place steaks on grill and reduce heat to medium. Cover and cook for 5 minutes. Turn-over and cook for an additional 5 minutes.
Reduce to low, top with 1 tomato slice, 1 basil leaf, 1 slice mozzarella, another basil leaf, and another slice of tomato.
Close the cover and grill for another 3-5 minutes. Remove to a platter and let rest for 5 minutes. Drizzle with olive oil and reduced balsamic vinegar before serving warm.