Make the sauce: whisk together mayonnaise, yellow mustard, honey, and optional BBQ sauce in a small bowl. Refrigerate until ready to serve.
Marinate the chicken: in a large bowl combine the cut chicken pieces, beaten egg, milk, and dill pickle juice if using. Cover and chill for 1 hour (or up to overnight) to tenderize.
Prepare the dry coating: pulse the plain breadcrumbs in a food processor until slightly finer. In a large shallow bowl, mix the flour, processed breadcrumbs, powdered sugar, paprika, white pepper, chili powder, and 1 teaspoon salt.
Heat the oil: place a large skillet over medium-high heat and add enough peanut or canola oil to reach about 1/2 to 1 inch depth. Heat until shimmering and hot (about 350°F to 375°F if using a thermometer).
Coat and fry the chicken: working in batches, remove chicken pieces from the marinade, let excess drip off, then dredge thoroughly in the flour mixture so each piece is evenly coated. Fry in the hot oil without overcrowding until golden and crispy, about 3–5 minutes per batch.
Drain and rest: transfer fried nuggets to a cooling rack set over a sheet pan to drain and stay crisp. Season with salt and pepper to taste while hot.
Serve: plate the nuggets and serve immediately with the chilled honey-mustard sauce.
