Preheat the oven to 425°F (220°C). Line a baking sheet with parchment paper and lightly spray with cooking spray.
Place each chicken breast between two sheets of plastic wrap and pound with a meat mallet or rolling pin until about 1/2 inch thick and even in thickness.
Season both sides of each chicken breast with salt and black pepper.
Place the flour in a shallow dish.
In a separate shallow bowl, whisk together the eggs and water until combined.
In a third shallow dish, combine the panko breadcrumbs, grated Parmesan cheese, garlic powder, and smoked paprika.
Dredge each chicken breast first in the flour, shaking off excess, then dip into the egg mixture, and finally coat thoroughly with the panko mixture, pressing gently to adhere.
Place the coated chicken breasts on the prepared baking sheet. Lightly spray the tops with cooking spray to help them crisp.
Bake in the preheated oven for 18 to 20 minutes, flipping halfway through, until the chicken is cooked through and the crust is golden and crispy.
While the chicken bakes, prepare the dipping sauce by whisking together the soy sauce, rice vinegar, honey, and grated fresh ginger in a small bowl.
Remove the chicken katsu from the oven and let rest for 2 minutes.
Slice the chicken into strips and serve with the dipping sauce on the side. Garnish with toasted sesame seeds and chopped green onions if desired.