Cut the chicken breasts into approximately 1 to 1½-inch bite-sized pieces.
Whisk the milk, egg, and optional pickle juice in a bowl. Add chicken, cover, and refrigerate for 30 minutes to 2 hours.
Combine flour, cornstarch, powdered sugar, salt, paprika, garlic powder, onion powder, black pepper, and optional white pepper in a shallow bowl.
Remove chicken from the marinade, allowing excess liquid to drip off. Press each piece into the flour mixture and shake off excess. Rest on a wire rack for 5 to 10 minutes.
Heat approximately 1½ inches of peanut oil in a heavy-bottomed pot to 350°F.
Fry nuggets in small batches for approximately 3 to 5 minutes, turning occasionally, until golden brown and cooked to 165°F internally.
Transfer to a wire rack, allow the oil to return to temperature between batches, and serve warm with dipping sauce.