Begin by cutting the chicken breast fillets into bite-sized pieces, about 1-2 inches in size.
In a mixing bowl, whisk together the egg and water until well combined. In another bowl, mix the flour, onion powder, ground mustard, black pepper, garlic powder, and kosher salt.
Dip each piece of chicken into the egg mixture, allowing any excess to drip off. Then, coat the chicken in the flour mixture, pressing gently to ensure an even coating. Repeat for all pieces.
Heat vegetable oil in a frying pan or deep fryer over medium-high heat to about 2-3 inches deep. Test the oil by dropping a small piece of bread; if it sizzles, the oil is ready.
Carefully place coated chicken pieces into hot oil without overcrowding. Fry about 4-5 minutes on each side until golden brown and cooked through, flipping as needed.
Remove nuggets from oil and place on paper towels to drain excess oil. Allow to cool slightly before serving.