Preheat the broiler. Place a wire cooling rack inside a rimmed baking sheet. Cut the top shell of the lobster tails lengthwise down the middle with kitchen shears. Then, using a knife, cut all the way through the tails to split into 2 pieces. Place them flesh-side up on the prepared baking sheet.
Mix together the butter, parsley, shallot, lemon zest, 1/2 teaspoon salt and a few grinds of pepper in a small bowl until well combined.
Spread 2 teaspoons of the compound butter on the flesh of each lobster tail half. Broil until the shells turn a bright orange, the flesh is opaque and cooked through and the tails begin to curl, about 4 minutes.
Transfer the tails to a serving platter and top each half with another teaspoon of the compound butter (save the remainder for another use).
To thaw lobster tails, refrigerate them for 24 hours until completely thawed. Alternatively, place them in a large pot and cover with cold water until completely thawed, 1 to 2 hours.
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