Start with the curry sauce by heating oil in a large pot. Add onions and sauté until translucent (about 5 minutes).
Add carrots and potatoes, cooking for another 3 minutes.
Pour in the chicken stock and bring to a boil. Reduce heat and simmer for 15 minutes or until vegetables are tender.
Break the curry roux into pieces and add to the pot. Stir until completely dissolved. Simmer for 5 minutes until thickened.
For the chicken, set up three shallow dishes: one with flour, one with beaten eggs, and one with panko.
Season chicken with salt and pepper, then coat each piece in flour, dip in egg, and cover with panko, pressing gently to adhere.
Heat oil in a large frying pan to 350°F (175°C).
Fry chicken for 4-5 minutes per side until golden brown and cooked through.
Let chicken rest on paper towels for 5 minutes before slicing.
Serve sliced katsu over rice, topped with curry sauce.