Shell your lobster tails, or if you bought them frozen, thaw them.
Place your oven rack in the center. Preheat
For the lobster: Place each tail, shell side up, on a cutting board. Using a large, sharp knife, cut the shell straight down the center, starting at the tail and up to where the body was.
In a small bowl, mix the marinade together (parsley, garlic, Dijon, salt, pepper, olive oil and lemon juice). and chives or basil
Place your lobster tails on the baking sheet. Pour the liquid over the lobster meat.
Add 1 tablespoon of butter per lobster tail.
cook the tails on the grill, flesh side up. Close the hood and let them broil, 3 to 5 minutes, depending on the size, until the meat of the tail is opaque and firm to the touch.. at 40-45 degrees
Transfer to the plates. To make the lemon butter, take the remaining cooking liquid and add to a pot. Add the remaining 2 tablespoons of butter. Bring to a boil and remove from heat.
Pour over lobsters or in ramekins.