Chop off the top portion of the garlic head to reveal cloves. Place the garlic head onto a piece of tin foil and pour about a tbsp of olive oil on top. Wrap the foil around the garlic. Place in the oven and roast for 45 minutes, or until the garlic is golden brown and soft. Remove from the oven and allow to cool five minutes.
Squeeze the garlic out of the skin into a food processor. Add shallot, anchovy, Serrano chile, cilantro, parsley, oregano, butter, and blitz thoroughly. Add one egg and blitz again.
Keep the butter at room temperature if using right away, or store in the refrigerator for up to one week.
Lower the heat on the oven to 375F/190C.
Using kitchen shears or strong scissors, cut the top side of the lobster tail shells lengthwise, from open end to the base of the tail. Put the tail upside-down in the palm of your hand and squeeze to break the translucent bottom shell. Grip the sides of the shell and pull open by about an inch or two. Using your finger, gently pull the lobster meat apart from the shell and up through the crack you’ve created while still keeping the meat attached to the tail. Let the meat sit on top of the shell.
Slather chimichurri sauce on top of the lobster tails in a cast-iron pan, and bake for about six minutes (if using pre-cooked lobster tails, broil under low broiler setting for two minutes.)