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Combine the wine, lemon juice, shallot, garlic and half of the salt and pepper in a small saucepan set over medium-high heat. Bring to a boil and simmer until reduced to about 2 tbsp (30 ml).
Remove from the heat and cool for 1 minute.
Whisk the cold butter into the wine mixture, a few cubes at a time, until well combined; set aside and keep warm. Lay each lobster tail on its flat side; insert the tip of a heavy chef’s knife at the base of the tail.
Firmly press down to cut through the shell and three-quarters of the way through the meat. Spread the tails open like a book. Season the lobster meat with the remaining salt and pepper.
Turn the grill on. Select the program Fish and press OK . Lightly grease the cooking plates with cooking spray. Once the purple indicator light has stopped flashing, place the lobster on the grill and close the lid.
Cook until the indicator light has changed to yellow. Serve the lobster with the warm butter sauce and lemon wedges on the side.