Season pork chops generously with salt and pepper on both sides.
Set up breading station: place flour in one dish, beaten egg in another, and panko breadcrumbs in a third.
Coat each pork chop in flour, dip in beaten egg, then thoroughly coat with panko breadcrumbs, pressing gently to adhere.
Heat oil in a large skillet or deep fryer to 350°F (175°C).
Fry pork cutlets for 3-4 minutes per side until golden brown and cooked through; drain on paper towels.
In a separate pot, sauté onion, carrots, and potatoes until softened, about 8-10 minutes.
Add water to the vegetable pot and bring to a boil; reduce heat and simmer until vegetables are tender, about 15 minutes.
Stir in curry roux pieces until completely dissolved and sauce thickens, about 5 minutes.
Let fried pork cutlets rest for 2-3 minutes, then slice into strips.
Serve sliced tonkatsu over steamed rice and top with curry sauce.