Heat butter in a saucepan. Add leeks and Granny Smith apple, cover and simmer until tender, for about 5 minutes. Add the Calvados and reduce until almost evaporated. Stir in the cider vinegar, broth, apple cider and bring to a simmer.
Add the chicken and egg noodles to the broth, cover and cook until the chicken is cooked through, about 5 minutes. Skim off any fat which is floating to the surface, stir in the heavy cream, optional Gruyere and season, to taste, with salt and pepper. Garnish with chives.
Recipe courtesy of Michele Urvater