Preheat your oven to 400°F (200°C).
Season the chicken breasts with salt and pepper.
Dredge each chicken breast in flour, dip into the beaten eggs, and then coat with Panko breadcrumbs, pressing the breadcrumbs onto the chicken to adhere.
Place the breaded chicken on a baking sheet lined with parchment paper. Bake in the preheated oven for 20-25 minutes or until the chicken is golden brown and cooked through.
While the chicken is baking, prepare the curry sauce. In a large pan, heat the vegetable oil over medium heat. Add the chopped onion and garlic, sauté until softened.
Add the curry powder or Japanese curry roux blocks and cook for 1-2 minutes until fragrant (or dissolve). Add the diced carrots and potatoes to the pan, stirring to coat with the curry mixture.
Pour in the chicken broth, soy sauce, and honey. Bring to a boil, then reduce the heat and simmer until the vegetables are tender.
If the curry sauce is too thick for your liking, you can add a bit more broth or water, a few tablespoons at a time, until you reach the desired consistency. If the sauce is too thin, you can let it simmer uncovered for a bit longer to allow it to reduce and thicken. Keep an eye on it and stir occasionally. If you prefer a thicker sauce, you can mix 1-2 tablespoons of cornstarch with a small amount of water to make a slurry. Stir this into the simmering curry sauce and allow it to thicken. Season the curry sauce with salt and pepper to taste. Once the chicken is done baking, slice it into strips and serve over rice with the curry sauce on the side.