Cut the chicken breast into bite-sized pieces and set aside.

In a shallow dish, mix the flour, salt, and black pepper until evenly combined.

In a second shallow dish, whisk the milk and egg together until uniform.

In a third shallow dish, place the Panko bread crumbs (optional). If you are not using Panko, leave this dish empty — you will dredge the nuggets in the seasoned flour again after the egg wash.

Working with a few pieces at a time, dredge each chicken piece in the seasoned flour, shaking off excess. Dip the floured piece into the milk-and-egg mixture, then press it into the Panko to coat (or, if not using Panko, dredge again in the seasoned flour). Place coated pieces on a wire rack and let rest for a couple of minutes.

Heat oil in a deep skillet, pot, or fryer to 350°F (175°C). Do not overcrowd the oil when frying; leave space between pieces so they cook evenly. Fry the nuggets in batches, turning as needed, until golden brown and cooked through (until an internal temperature of 165°F / 74°C is reached or the center is no longer pink).

Use a slotted spoon or tongs to transfer cooked nuggets to a wire rack to drain. Repeat frying remaining batches, maintaining the oil temperature around 350°F.

Let the nuggets rest briefly on the rack before serving.