Brine chicken pieces: Stir together pickle juice and granulated sugar in a medium bowl until sugar dissolves. Add chicken breast pieces; cover and chill 30 minutes. Remove from bring, and pat dry.

Mix ingredients for coating: Whisk together buttermilk, cayenne, and egg in a shallow dish. Whisk together flour, cornstarch, powdered sugar, powdered milk, salt, pepper, paprika, baking powder, and baking soda in a second shallow dish.

Coat chicken pieces: Dredge brined chicken pieces in flour mixture to coat and shake off excess. Toss chicken in egg mixture to coat, and then back to flour mixture to dredge again. Press flour mixture to adhere to chicken, and place on a wire rack. Chill 15 minutes.

Heat peanut oil: Heat oil to 325°F in a Dutch oven over medium-high.

Fry chicken: Carefully add chicken pieces to hot oil in 3 batches, turning often to ensure even browning. Cook until cooked through, about 6 to 8 minutes. Let drain on a wire rack set in a baking sheet lined with foil or paper towels.

Bake rolls: Meanwhile, bake frozen Parker House Rolls according to package directions.

Make honey-butter mixture Once you remove the foil to continue baking, stir together melted butter and honey. Brush honey butter over tops of rolls and continue baking 5-10 minutes or until golden brown.

Stuff rolls: Remove from oven and split rolls in half. Add cooked chicken nuggets to rolls and serve immediately.