Sprinkle beef with salt and pepper. Melt butter with 1/4 cup olive oil in large pan. Add beef and cook until medium rare, about 20 minutes. Cool for at least 3 hours in the refrigerator.
Add olive oil, basil, tomato and garlic to a bowl. Mix and let sit for at least 30 minutes. Slice steak as thin as possible and serve with tomato sauce.
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