let’s prepare the herb butter in a small bowl by blending the butter, shallots, hot sauce, and black pepper. Mix well, cover set aside until it is needed.
Preheat the grill to medium-high.
With kitchen shears, or a sharp knife, cut the lobster shell straight down the middle the length of the shell, avoiding the meat and stopping before you get to the fanned-out end of the tail. Carefully pull the shell apart to expose the meat.
Using your fingers, gently but firmly, pry the meat away from the shell and the membrane that is on the belly, pull the meat out of the shell, leaving the very end by the tail attached. Put the meat back into the shell.
Brush the meat with olive oil and season with a little salt. Grill the lobster’s meat-side down for about 5 mins. Turn the tails over and spoon a generous TBSP of herbed butter onto the meat. Grill for another 4 mins, or until the flesh is an opaque white color. Don't overcook it, when it's white, it's done.
Remove the lobster tails from the grill and serve immediately with more herb.