For the dressing, combine the crème fraîche, cider vinegar, extra virgin olive oil, Dijon mustard and season to taste. Boil the new potatoes in salted water for 20 minutes.
Meanwhile, slice the chicken breasts into finger length strips, toss in the olive oil. Add some salt and pepper to season.
Heat a griddle pan or a non-stick frying pan until almost smoking, then add the chicken strips. Turn chicken after 1-2 minutes, or until they easily lift away. Sear on all sides, until cooked through. Remove and put to one side.
Roughly slice the lettuce and place in a large salad bowl. Add the cherry tomatoes, ham and cheese. Drain the potatoes, cool in cold water. Quarter the potatoes and add to the salad, along with the cooked chicken.
Drizzle with dressing and scatter some roughly chopped parsley.