Cut chicken breasts into uniform 2-inch pieces. Place the chicken in a bowl and cover with dill pickle brine, ensuring all pieces are submerged. Marinate in the refrigerator for at least 30 minutes, or up to 4 hours.

In a shallow dish, combine the flour, powdered sugar, salt, and pepper for the dry dredge, mixing well.

In a separate shallow dish, whisk together the milk and egg for the wet dredge.

Heat 2 cups of oil in a deep pot or Dutch oven over medium-high heat to 350°F (175°C). Use a kitchen thermometer to monitor the temperature.

Working in small batches, remove chicken pieces from the pickle brine, allowing excess liquid to drip off. First, dredge each piece thoroughly in the dry flour mixture, pressing to coat well. Then dip into the egg-milk mixture, and finally back into the dry flour mixture, pressing firmly again to create a thick, craggy coating.

Carefully lower the breaded chicken pieces into the hot oil, ensuring not to overcrowd the pot. Fry for 3-5 minutes, turning occasionally, until golden brown and cooked through (internal temperature reaches 165°F/74°C).

Using a slotted spoon or spider, remove the fried nuggets from the oil and place them on a wire rack set over paper towels to drain excess oil. Immediately season lightly with a pinch of salt.

Repeat the frying process with the remaining chicken pieces, ensuring the oil temperature returns to 350°F (175°C) between batches. Serve hot with your favorite dipping sauce.