How do I thicken my Japanese curry after the fact?
Several options, depending on the type of curry and the ingredients already present.
Japanese Style Curries
Using a commercial, packaged Japanese-style roux:
Add another brick or two from the package. This type dissolves nicely generally with minimal clumping.
Using a homemade, Japanese style roux:
You can prepare additional roux by melting fat (butter, beef fat, etc) in a saucier, foaming it if needed (as with butter), and whisking in flour (we usually use a 1:1 ratio). Allow the flour to brown to the desired level, keeping in mind that the thickening power decreases the darker it gets. If you prefer not to use flour, potato starch/katakuriko is a reasonable alternative. When suitably dark, take some of the liquid from your existing curry and mix in to the roux, whisking vigorously to minimize the risk of clumping. Add more of the existing curry liquid if you think there's a risk of clumping, then reintegrate it back into the main pot. (if you were starting this roux from scratch you'd also integrate fat-cooked spices into the roux, but your problem does not appear to be flavor).
Avoiding fussiness:
Mix cornstarch or potato starch (katakuriko) in cold water. Once reasonably dissolved, add it to the curry pot. This type of thickener can create a slightly odd texture in a Japanese curry, as the browned roux creates a more velvety texture, but that doesn't mean I haven't done it before in a pinch. The liquid will thicken as it boils.
Indian Style Curries
For more Indian-style curries, there are other options.
If your curry contains lentils, chickpeas or potatoes:
Smash some of them in a small bowl, or just against the edge of the pan. Allow the pot to boil a bit.
If you have almonds, cashews or similar nuts available:
Grind a small quantity of nuts in a coffee/spice mill, and incorporate them into the curry. These need to boil more gently, and I usually do this sauce more intentionally by making them the focal point (dum ki ghom, for example, which has mushrooms and tomato puree in a nut sauce) but can rescue an existing curry too.