Heat a griddle pan over a high heat until smoking hot. While it’s heating up, put the chicken pieces between 2 pieces of baking parchment and bash with a rolling pin to flatten. Unwrap the chicken and brush the pieces with olive oil.
Cook the chicken on the griddle pan until cooked through, turning once – this should take about 10 mins. Transfer the chicken to a plate, pour over a little of the lemon juice and season.
Put the rolls on the griddle pan, cut- side down, to lightly toast them. In a small bowl, stir together the mayo and remaining lemon juice. Build your burgers with the chicken, egg slices, lettuce, a dollop of the mayo mixture, the cress and Parmesan shavings.