Brush the leeks with the hazelnut oil. Cook, in batches, on a preheated hot ridged griddle pan or under a preheated hot grill, turning frequently, for 6–8 minutes until evenly browned and cooked through. Toss with the lemon juice and season with salt and pepper. Leave to cool.
Meanwhile, heat a heavy-based frying pan until hot, add the hazelnuts and cook over a medium heat, stirring, for 3–4 minutes until browned. Leave to cool slightly and then roughly chop. Separate the lettuce leaves and pull the mint leaves from the sprigs.
Arrange the leeks in serving bowls or on plates and top with the lettuce leaves, mint and hazelnuts. Whisk all the dressing ingredients together in a small bowl, season with salt and pepper and pour over the salad. Shave the pecorino over the salad and serve garnished with the olives.