Heat neutral oil in a large pan over medium heat. Stir-fry onion, celery, carrot, and mushrooms until soft and fragrant, about 5-7 minutes.
Add ground pork, salt, and freshly ground black pepper. Cook until meat is browned and cooked through, breaking up any large chunks, about 8-10 minutes.
Pour in chicken stock and water. Bring to a simmer and cook until vegetables are tender, about 8-10 minutes.
Stir in curry powder, curry roux cubes, butter, ketchup, and tonkatsu sauce. Simmer while stirring until roux dissolves completely and mixture thickens, about 5 minutes.
Serve hot over steamed Japanese short-grain rice, topped with fried eggs if desired.