Preheat oven to 200°F.
Working 1 breast at a time, butterfly the chicken by cutting horizontally with a sharp knife almost all the way through. Open like a book and pound each piece between sheets of plastic to about 1/8-inch thick. Season with salt and pepper.
Set up a breading station: Place the flour, some salt and pepper in a shallow dish. In another, beat the eggs, milk and mustard, and season. Place the breadcrumbs in a third dish with the nutmeg and salt.
Heat 1/8 inch oil in a large skillet over medium to medium-high. Working in two batches, coat the chicken in flour, then the egg, then the breadcrumbs, pressing to adhere. Fry chicken until deep golden and cooked through, about 3 minutes per side. Transfer the schnitzel to a wire rack set on a baking sheet and keep warm in the oven.
For the schn’apple, heat another large skillet over medium to medium-high. Add the butter. Once melted, add the apples, sliced fennel and onions; 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 topped with fennel mixture and lemon wedges alongside.
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