On a plate, season flour with 1/4 teaspoon salt. In a shallow dish, whisk egg with 1 tablespoon water. On another plate, season panko with 1/2 teaspoon salt and 1/4 teaspoon pepper. Pat chicken dry. Dredge chicken in flour, then dip in egg, letting excess drip off. Coat with panko, pressing gently to adhere.
In a large nonstick skillet, heat oil over medium. Add chicken; cook until golden brown and cooked through, 8 to 10 minutes total, flipping once. In a small bowl, whisk buttermilk, mayonnaise, vinegar, and parsley; season with salt and pepper. Arrange lettuce, apples, and cranberries on a platter. Slice chicken, add to platter, and drizzle with dressing.