Preheat the oven to 200°.
Working with 1 breast at a time, butterfly the chicken by cutting horizontally [1, above] with a sharp knife almost all the way through [2, above]. Open like a book [3, above] and pound between sheets of plastic to about 1/8 inch thick. Season with salt and pepper.
Set up a breading station: Place the flour in a shallow dish; season. In another shallow dish, beat the eggs, milk and mustard; season. Place the breadcrumbs in a third shallow dish; season with the nutmeg and salt.
In a large skillet, heat 1/8 inch oil over medium to medium-high. Working in two batches, coat the chicken in the flour, then the egg, then the breadcrumbs, pressing to adhere. Fry until deep golden and cooked through, about 3 minutes per side. Transfer the schnitzel to a wire rack set inside a baking sheet; keep warm in the oven.
Meanwhile, for the schn’apple, heat another large skillet over medium to medium-high. Add the butter. When it melts, add the apples, sliced fennel and onion; season with salt and cook, stirring often, until crisp-tender, about 5 minutes. Stir in the schnapps and toss in the fennel fronds and dill.
Serve the schnitzel with the fennel mixture and lemon wedges.