Begin by preparing the chicken. Season the chicken breasts with salt and pepper. Set up a breading station with three shallow dishes: one with flour, one with beaten eggs, and one with panko breadcrumbs.
Dredge each chicken breast in flour, shaking off excess, then dip in the egg, and finally coat with panko breadcrumbs. Press the breadcrumbs onto the chicken to ensure an even coating.
In a large skillet, heat about 1/2 inch of vegetable oil over medium heat. Once hot, carefully add the breaded chicken breasts and fry for about 4-5 minutes on each side, or until golden brown and cooked through. Remove and drain on paper towels.
In another pot, heat a tablespoon of oil over medium heat. Add the diced onion, garlic, and ginger, and sauté until the onion is translucent.
Add the sliced carrots and diced potato to the pot, stirring for a few minutes. Pour in the chicken broth, curry powder, soy sauce, and honey. Bring to a simmer and cook until the vegetables are tender, about 15 minutes.
Stir in the cornstarch mixture to thicken the sauce, cooking for an additional 2-3 minutes until it reaches your desired consistency.
Slice the fried chicken katsu into strips and serve over cooked white rice, topped with the curry sauce and garnished with chopped green onions.