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Season filets with salt and pepper and lightly brush with olive oil
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Heat grill to high. Place steaks on grill, reduce heat to medium. Cover and cook for 5 minutes.
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Flip and cook for an additional 5 minutes.
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At this point you have two options. Remove steaks from the grill and top with one tomato slice, one basil leaf, one slice mozzarella, another basil leaf, and another slice of tomato and serve as is. Or you can reduce heat to low, top with one tomato slice, one basil leaf, one slice mozzarella, another basil leaf, and another slice of tomato. Then close the cover and grill for another 3-5 minutes or to desired doneness.
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Remove to a platter, let rest for at least 5 minutes, drizzle with reduced balsamic vinegar before serving.