For the aioli:
Put the egg yolks into a medium bowl with the mustard and wine vinegar and whisk together, then start to add the olive oil bit by bit until evenly combined. Add the crushed garlic, whisking continuously as you do so to emulsify the mixture. Once all the oil is added you should have a thick, glossy mayonnaise. Season with salt and add a squeeze of lemon juice to taste.
For the langoustines:
Pre-heat the oven to 180C/Gas Mark 4. Heat a heavy-bottomed, oven-proof pan containing the olive oil. Add the langoustines and cook for about 2-3 minutes, turning them halfway through. Place the pan in the oven and roast for 3 minutes at 180C/Gas Mark 4. Season with salt and pepper.
Serve in a bowl or pint glass with some crusty fresh bread, the aioli and fresh slices of lemon.