Flatten the chicken breasts slightly with a meat mallet. Brush with olive oil and season.
Preheat a grill pan until hot and cook chicken for 10-15 minutes, turning once. Remove from the heat and set aside to rest..
To make the dressing, pound the garlic and anchovies in a mortar and pestle or blend using a hand blender.
Place in a bowl and add the egg yolk, mustard, lemon juice and seasoning.
Whisk in the oil slowly to make a thick creamy dressing.
Cut the warm chicken into chunky strips and tip into the bowl with the lettuce.
Throw in the parmesan shavings and enough dressing to coat and toss well.
Place a good handful of the mixture onto each of the flour tortilla wraps and fold over one end before rolling up. Serve immediately.