Set up a breading station with three shallow dishes: one with the flour, one with the beaten eggs, and one with the panko breadcrumbs mixed with the salt and pepper.

Dredge the chicken pieces in the flour, dip them in the egg, and then coat them in the panko mixture, pressing to adhere.

In a large skillet or Dutch oven, heat 1-2 inches of vegetable oil to 350°F.

Fry the breaded chicken nuggets in batches for 2-3 minutes per batch, or until golden brown and cooked through.

Drain the chicken nuggets on a paper towel-lined plate and serve hot.