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 you have a smooth paste, then add the butter and lemon juice and blitz for 1 minute.
Season the lobster, then place under the grill, flesh side up, or if using a grill plate or barbecue 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 lovely smoky, herby flavour.
Keep basting the lobster until it is cooked through, which should take no longer than a further 5–6 minutes.
Serve with a simple salad of leaves – rocket is my favourite – dressed with lemon juice and olive oil.