Cut chicken breasts into roughly 1-inch bite-sized cubes, keeping them as uniform as possible for even cooking.
Add chicken pieces to a large zip-top bag with pickle juice and milk. Refrigerate for at least 30 minutes and up to 2 hours.
Whisk together flour, breadcrumbs, powdered sugar, garlic powder, paprika, baking powder, salt, and pepper in a wide bowl. In a separate bowl, whisk egg with remaining milk.
Drain marinade from chicken. Coat each piece in flour mixture, pressing firmly. For extra crunch, dip in egg wash and dredge a second time in flour.
Heat peanut oil in a heavy skillet to 350°F (175°C). Maintain this temperature for optimal crispiness.
Fry nuggets in small batches for 3-4 minutes, turning once, until golden brown and internal temperature reaches 165°F (74°C).
Transfer fried nuggets to a wire rack to drain. Allow oil to return to temperature between batches.
Whisk together mayonnaise, honey, mustard, barbecue sauce, and lemon juice until smooth. Adjust seasonings to taste.
Serve nuggets immediately with homemade Chick-fil-A sauce and your favorite sides.