Place chicken cubes in a bowl with pickle juice and 1/4 cup milk; cover and refrigerate for 30 minutes to allow the brine to tenderize the meat.
In a shallow bowl, whisk together the eggs and the remaining 1/4 cup milk to create an egg wash.
In a separate large bowl or heavy-duty zip-top bag, whisk together the flour, powdered sugar, salt, black pepper, paprika, garlic powder, and celery salt until fully homogenous.
Drain the chicken from the brine and discard the liquid; pat the chicken pieces slightly with paper towels to remove excess moisture.
Dip the chicken pieces into the egg wash, then transfer them to the flour mixture and shake vigorously until each piece is thoroughly and evenly coated.
Heat the peanut oil in a heavy-bottomed Dutch oven or deep fryer to exactly 350°F (177°C).
Fry the chicken in small batches for 3 to 5 minutes per batch, maintaining oil temperature, until the internal temperature of the nuggets reaches 165°F (74°C) and the exterior is golden brown.
Remove nuggets with a slotted spoon and transfer to a wire cooling rack set over a baking sheet to drain and maintain crispness for 2 minutes before serving.