Start by making the aïoli. Smash the garlic and salt together in a pestle and mortar. Whisk together the egg yolk and mustard in a bowl, then start adding the olive oils, bit by bit.
Once you’ve blended in 150ml, add the rest in larger amounts. Finally add the smashed garlic, then lemon juice, salt and pepper to taste.
Lay your langoustines flat on a chopping board and, with a sharp knife, saw through their shells lengthways – cutting three-quarters, not all, of the way through. Open them out in a butterfly style and flatten them down gently with the heel of your hand.
Season the langoustines and cook them, cut-side down, across the bars (so they don’t fall through) on a hot barbie for 2 minutes and then for 30 seconds on their backs before lifting them on to a serving plate.
Sprinkle with torn fennel tops, if using, and serve with the lemony aïoli.