I just did some quick investigating and basically the gravy is just a beef broth gravy. Some recipes call for a bit of onion and/or mushroom but I think the "secret" to Hawaiian loco moco gravy is a dash of soy sauce instead of salt.
I start with a standard roux of equal weight of flour and butter and then whisk that into the broth. The broth needs to be hotter than the roux to prevent lumps. 3T flour + 2T butter will thicken 1C of liquid. Make sure to cook the roux for a bit until the flour smell is gone otherwise it will taste like flour. The darker the roux, the less it will thicken.
