Whisk together mayonnaise, yellow mustard, honey, and optional BBQ sauce in a small bowl; refrigerate until ready to serve.
In a large bowl combine the beaten egg, milk, and dill pickle juice (if using). Add the cut chicken pieces, cover with plastic wrap, and chill in the refrigerator for 1 hour or up to overnight.
Place the plain breadcrumbs in a food processor and pulse a few times to break them up, then transfer to a large shallow bowl.
In the same large shallow bowl, add the all-purpose flour, powdered sugar, paprika, white pepper, chili powder, and 1 teaspoon salt. Stir until evenly combined.
Heat about 1–2 inches of oil in a large skillet over medium-high heat until hot but not smoking (around 350°F/175°C).
Working in batches, dredge the chilled chicken pieces in the flour-breadcrumb mixture, shaking off excess, then carefully add to the hot oil without overcrowding the pan.
Fry the chicken until golden brown and cooked through, about 3–5 minutes per batch depending on piece size. Use tongs or a slotted spoon to turn as needed.
Transfer the cooked nuggets to a cooling rack to drain excess oil, season with additional salt and pepper to taste, and serve immediately with the chilled sauce.