Remove the loose, papery outer skin from the heads of garlic. Using a sharp knife, cut about ½ inch off the top to expose the cloves. Place each garlic head on a large square of heavy-duty aluminum foil and drizzle 1 tablespoon of the olive oil over the top of the cloves. Fold up the foil sides and seal to make a packet, leaving a little room for the expansion of steam. Brush the cooking grates clean. Grill the packet over indirect medium heat, with the lid closed, until the cloves are soft, 45 minutes to 1 hour. Set aside to cool.
Spread the paste evenly on both sides of the steaks. Cover with plastic wrap and refrigerate for 2 to 4 hours. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
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. Serve warm.
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