In a bowl of a food processor combine the sauce ingredients. Pulse until you get a semi-smooth consistency. Season with salt and pepper. Transfer to a small bowl and set aside.
In a small bowl mix the rub ingredients. Lightly brush the steaks on both sides with oil and season evenly with the rub. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
Prepare the grill for direct cooking over high heat (450° to 550°F).
Brush the cooking grates clean. Grill 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. Serve warm with the sauce.
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