Lay a turkey steak between 2 sheets of clingfilm and pound lightly with a mallet until about 1 cm (½ inch) thick. Repeat with the remaining steaks.
Spread the pesto over each beaten turkey steak and lay 1 slice of Parma ham on top of each. Sprinkle the tomatoes and mozzarella evenly over the turkey steaks, then season to taste with salt and pepper and roll up each one from the long side.
Cut the turkey rolls into 2.5 cm (1 inch) slices. Carefully thread the slices of roll evenly on to 4 metal skewers.
Brush the turkey rolls lightly with the oil and grill under a preheated grill for 6 minutes on each side or until cooked through. Increase or reduce the temperature setting of the grill, if necessary, to ensure that the rolls cook through and brown on the outside. Garnish with chopped parsley and serve hot with lemon wedges for squeezing over.