Preheat the grill or barbecue to hot. Place the lobster on a chopping board.
Insert a large, sharp, heavy knife into the cross on the back of the head and cut down towards the tail, cutting it in half
Remove the stomach and the black intestinal tract (if there is one) that may run through the middle of the tail and discard
Place all the remaining ingredients (including salt and pepper to taste) except the olive oil and lemon juice in a food processor and blitz until it has the consistency of a smooth paste, then add the butter and lemon juice and blitz for an additional minute
Season the lobster, then place under the grill, flesh side up (if using a grill plate or barbecue, place flesh side down) and cook for 4-5 minutes
Brush the flesh with the olive oil. If cooking on a barbecue, stoke the fire with a rosemary sprig
If cooking on a barbecue, place an upturned heavy casserole over the top of the lobster to give it a smoky, herby flavor
Keep basting the lobster until it is cooked through, about 5-6 minutes