Heat grill to medium and line the grill pan with foil. Beat the egg white on a plate with a little salt and pepper. Tip the parmesan onto another plate. Dip the chicken first in egg white, then in the cheese. Grill the coated chicken for 10-12 mins, turning once until browned and crisp.
Meanwhile, boil the potatoes for 10 mins, adding the peas for the final 3 mins, then drain. Toss the vegetables with the spinach leaves, vinegar, oil and seasoning to taste. Divide between four warm plates, then serve with the chicken.