Pour the oil into a large skillet and heat over medium until hot but not smoking.
Beat the eggs with 1 teaspoon water in a bowl and set aside.
Place the whole wheat flour on a small plate for dredging.
In a mixing bowl combine the panko, grated Parmesan, kosher salt, chopped rosemary, garlic powder, onion powder, paprika, chili powder, and lemon zest; mix well.
Cut the chicken into 1-inch cubes and lightly coat each piece with flour, shaking off excess.
Dip the floured chicken pieces into the beaten egg, letting excess drip off, then press each piece into the panko-Parmesan mixture until evenly coated.
Fry a few coated chicken pieces at a time in the hot oil for about 5 minutes per side, or until golden brown and cooked through (no pink inside), turning once.
Transfer cooked nuggets to a paper towel-lined plate to drain and repeat with remaining chicken.
Serve immediately with honey mustard or marinara for dipping, if desired.