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Make the butter by mixing together all the ingredients, then season and set aside. Can be made two days ahead. Remove from the fridge to soften before using.
Use kitchen scissors to cut along the tops of the lobster shells, then flip the tails over and crack the ribs of the shell. Use your fingers to open the shell and loosen the meat keeping it attached at the base and pull it half out. Use a knife to cut along the top of the tail without cutting all the way through and remove the vein if you see one. Sit the tail in a shallow roasting tray and add some butter to each one. Tails can be prepared a few hours ahead and chilled.
Heat the grill to high, then grill the lobster tails for 10 mins until cooked through. Put them on plates and drizzle with the butter from the pan, or pour the butter into a ramekin and put it in the middle of the table for dipping the lobster meat in. Serve with lemon wedges and scatter with extra parsley, if you like.