Strip the leaves from the thyme sprigs and reserve the stems for later. Finely chop enough of the leaves to give you 2 tablespoons of chopped thyme. Mix the thyme leaves in a small bowl with the remaining paste ingredients, including 1 teaspoon salt and ¼ teaspoon pepper.
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Chopping Thyme
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Brush the paste evenly over both sides of the steaks. Cover and refrigerate for 2 to 4 hours.
Soak the wood chips in water for at least 30 minutes.
Remove the steaks from the refrigerator and season evenly with ½ teaspoon salt and ¼ teaspoon pepper. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
Prepare the grill for direct cooking over high heat (230° to 290°C).
Prepare the grill for cooking over high heat (260°C).
Brush the cooking grate clean. Drain and add the wood chips and thyme stems to the charcoal or to the smoker box of a gas grill, following manufacturer's instructions, and close the lid. When smoke appears, grill the steaks over direct high heat, with the lid closed, 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.
Brush the cooking grate clean. Drain and add the wood chips and thyme stems to the charcoal or to the smoker box of a gas grill, following manufacturer's instructions, and close the lid. When smoke appears, grill the steaks over high heat, with the lid closed, 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.