Preheat a medium saucepan over medium-high heat. Add the apples, lemon juice, cider, brown sugar, ginger and cinnamon and stir. Cook, stirring frequently, until mushy, about 15 minutes. Remove the ginger.
While the applesauce is cooking, sprinkle a little water into each of 4 quart-size plastic storage bags. Place 1 chicken breast in each bag, push out the excess air and seal it up. Using a heavy-bottomed pot, pound each breast until evenly thin, just shy of busting out of the bag.
Place the pretzels, bread crumbs, cheese, thyme, nutmeg and pepper in a food processor and pulse to grind until theyre the consistency of bread crumbs. Transfer the ground pretzels and cheese to a shallow dish.
Crack the egg into a second shallow dish and lightly beat with a splash of water. Place some flour in a third dish. Coat the chicken first in flour, then egg and finally in cheese and pretzel crumbs.
In a large skillet, heat 1/4 inch of oil over medium-high heat and add the coated chicken breasts. Cook in a single layer, 3 or 4 minutes on each side, until the juices run clear and the breading is evenly browned. Cut off a piece of a cutlet and taste, to see if you want to salt them a little. Serve the chicken with the applesauce.