Preheat the grill to high. Put the bagels, cut-side up, on the grill tray and grill for 3–4 minutes until golden brown and toasted.
Meanwhile, lightly beat the cream cheese, gherkins and parsley together in a small bowl.
Divide the cheese mixture into eight portions and spread over the toasted side of each bagel half.
Place a lettuce leaf on the bottom half of each bagel, folded to fit, then top with a thick slice of tomato followed by one-quarter of the turkey and pastrami, loosely folded. Put the tops back on the bagels and press together. Cut in half to serve.