I haven't made katsu for a while, I based mine on a recipe in the NYT (who have excellent recipes, alas paywall) – but it's mostly curry powder, garlic, ginger, onion, carrot, nutmeg, soy sauce, and a dash of coconut cream. I call this 'chip shop curry sauce.' The NYT don't.
It should be a little coconutty, not an entire can. Cook down the carrot, onion, garlic, and ginger (for a good 20-30 minutes on a low heat), add the nutmeg and curry powder, deglaze with soy sauce and stir in the coconut cream (a dash of water or stock as required) and cook till everything is the right consistency. I also rarely bother with added sweet – if you cook down the onions till they're caramelizing, that's sweet enough. I don't blend, I like it lumpy, and the veg bits have mostly broken down. Sometimes, for japes, I throw in some Szechuan pepper. You do need a lot more ginger than you think, it loses its edge when you cook it for a while.
It also works well as a sauce for slow cooked duck or chicken (boned) without the breading. Just do it in a casserole and or pan on a low heat and cook for about two hours until everything is falling apart.
