Place the boneless, skinless chicken breasts between two sheets of plastic wrap. Use a meat mallet or rolling pin to gently pound the chicken to an even thickness of about 1/2 inch.
Sprinkle kosher salt and ground black pepper over both sides of the chicken breasts, ensuring they are well seasoned.
In three shallow dishes, prepare the coating: place the flour in the first dish, beaten eggs in the second, and Panko breadcrumbs in the third.
Dredge each chicken breast in flour, shaking off excess, then dip into beaten eggs, allowing excess to drip off. Coat the chicken in Panko breadcrumbs, pressing gently to adhere.
Heat the vegetable oil in a heavy-bottomed skillet over medium heat. Use a cooking thermometer to reach 350°F (175°C) for frying.
Carefully place the breaded chicken breasts into the hot oil. Fry 4-5 minutes per side until golden brown and cooked through (internal temperature 165°F/75°C).
While frying, whisk together ketchup, Worcestershire sauce, oyster sauce, and granulated sugar in a small bowl. Adjust sweetness or tanginess to taste.
Transfer cooked chicken to paper towels to drain excess oil. Slice and serve drizzled with sauce, paired with rice and steamed vegetables.