Peel and dice the onion, carrot, and potato into small, uniform bite-sized pieces.
In a small saucepan, sauté the onion in a tablespoon of water until soft, then add the carrots, potatoes, and 1.5 cups of water.
Bring the liquid to a boil, then reduce heat and simmer for 10 minutes until the vegetables are fork-tender.
Turn off the heat, add the Japanese curry roux block, and stir continuously until the roux is fully dissolved and the sauce thickens into a velvety consistency.
Butterfly the chicken breast to an even thickness and season both sides with sea salt and black pepper.
Set up a dredging station with flour in one bowl, beaten egg in the second, and panko breadcrumbs in the third.
Coat the chicken in flour, dip into the egg, and press firmly into the panko until fully crusted.
Lightly spray the breaded chicken with avocado oil and air-fry at 400°F for 12 minutes, flipping halfway through, until golden and crispy.
Slice the katsu into thick strips and serve immediately over the warm curry sauce and a small portion of rice.