Prepare the grill for direct cooking over high heat (450° to 550°F).
Lightly brush the steaks on both sides with oil and season evenly with salt and pepper. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
In a medium bowl whisk the shallot, vinegar, mustard, ¼ teaspoon salt, and ¼ teaspoon pepper. Slowly whisk in 2 tablespoons of oil, forming a smooth vinaigrette. Add the tomatoes and basil. Mix well.
Brush the cooking grates clean. Grill the steaks over direct high heat, with the lid closed as much as possible, until cooked to your desired doneness, 6 to 8 minutes for medium rare, turning once or twice (if flare-ups occur, move the steaks temporarily over indirect heat). Remove from the grill and let rest for 3 to 5 minutes. Add the cheese to the vinaigrette. Mix gently. Serve the steaks warm with the vinaigrette spooned over the top.
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