Place the flour in a shallow dish; season with salt and pepper. In another shallow dish, whisk the eggs; season. In a third shallow dish, mix the panko, cheese, breadcrumbs, parsley, granulated garlic and oregano.
In a large, shallow skillet, heat 1/8 to 1/4 inch oil over medium-high. Coat the chicken in the flour, then the eggs, then the breadcrumb mixture, pressing to adhere. When the oil begins to ripple and smoke, add half the chicken. Cook until deep golden and cooked through, about 3 minutes per side. Transfer to paper towels or a wire rack to drain; season. Repeat with the remaining chicken.
In a small bowl, mix the ketchup and balsamic vinegar.
Serve the nuggets with the balsamic ketchup.