Brine the chicken. In a large bowl or zip-top bag, combine the cubed chicken, pickle juice, and ½ cup of the milk. Refrigerate for at least 1 hour (or up to overnight).
Drain and dry. Pour the chicken into a colander, discard the brine, and pat the pieces dry with paper towels.
Egg wash soak. Whisk the eggs with the remaining ½ cup of milk in a shallow bowl. Add the drained chicken and let it sit for 20–30 minutes.
Mix the breading. In a second shallow bowl, whisk together the flour, powdered sugar, salt, white pepper, and chili powder.
Preheat. Preheat the air fryer to 370°F (188°C) for 3 minutes. Lightly mist the basket with olive oil spray.
Dredge. Working a few pieces at a time, lift the chicken from the egg wash, let excess drip off, and toss in the flour mixture, pressing gently to coat. Transfer to a plate.
Cook, batch 1. Arrange the nuggets in a single layer in the basket with ½ inch between each. Mist generously with olive oil spray.
Air fry. Cook at 370°F for 6 minutes. Flip each nugget, mist the second side, and increase the temperature to 390°F (199°C). Cook for another 4–6 minutes, until the breading is deep golden and the internal temperature reads 165°F (74°C).
Repeat with any remaining chicken.
Serve immediately with copycat Chick-Fil-A sauce, honey mustard, or your favorite dip.