I am vegan. I want to make a vegan gravy sauce but I want to make my own vegetable broth without too much salt. I don't want to use a ready to use vegetable stock and nutritional yeast. How can I add a rich flavor specifically suited to a gravy, with as much umami as possible?
A gravy tastes like gravy because it has salt and glutamates, which is what yeast extract has been formulated to deliver. There is no vegan replacement. The only good way to produce glutamates in your kitchen is to sear meat.
You can certainly make a veloute sauce instead of a gravy. It is made from stock and roux. Roux is a combination of fat and starch - the standard is flour with butter, but any fat and any starch works. A veloute sauce has great texture, but the taste is quite bland. You can strengthen the taste by using mushroom stock instead of vegetable stock, use flavored oils (e.g. macadamia nut oil), and herbs and spices. It will develop a complex aromatic profile, but it will stay very far from the rich umami of a gravy. The aromatic oils and fresh herbs also tend to be somewhat expensive.
If you are set on making a gravy, you could use pure MSG instead of the yeast extract. This will give you a very good taste, but I don't know if it will improve your situation. First, MSG is not so easily available, and I don't know if they also offer it in guaranteed animal-free versions. It isn't usually derived from animal products, but as a vegan you are probably sensitive for the possibility of contaminations. Second, if you don't add the salt by yourself, you will still be missing out on taste. This is not that bad by itself, because maybe you are OK with a product which has a higher glutamate to salt ratio than what you can get with yeast extract or bouillon cubes - personal preferences for salt vary. But, if you are avoiding salt, chances are that you are on a low-sodium diet. And MSG is a sodium compound by itself, so you'd have to restrict it too. If that's the case, you're better off using small amounts of yeast extract and living with less taste than combining MSG and salt by yourself.
You could finally try to get umami from plant sources, but this is not so easy. The only two plants in question are tomatoes and mushrooms. Concentrated tomato puree makes great sauces, but they taste like tomato, not like gravy, and there is no way to remove the tomato taste from them. So you're left with mushrooms only, preferably shiitake and relatives. They're OK, but they are mostly water. You'd have to get dehydrated mushroom powder and use it in copious amounts. Because dehydrated mushrooms aren't that smooth, you'll never get a perfectly smooth texture. Your sauce will also be quite expensive. On the upside, the compound in shiitake which gives them their umami taste is not sodium based.
Your last options would be seaweed and wheat-based fake beef flavoring agents. I don't know where you could get hold of seaweed or how you'd have to prepare it, and also whether you can make a gravy with it without a fishy smell. The fake beef flavoring agents are an industrial food additive, I've never heard of it being available for consumers.
Mushrooms (esp Shiitake), tahini, tomatoes, miso, gochunjang/doubanjang, furu/sufu, seaweed, (brewed) soy sauces, fermented soybean or wheat pastes, shiitake/shiitake soy sauce can all bring umami (some Types of Doubanjang or fermented tofu might not be vegan, check what brand you use...). The one problem for extreme umami is that it works even better with guanylates/inosinates present, and these are usually only found in animal sources - rumours have it that Golden Mountain sauce, even when containing these - not all variants seem to do, differing ingredient lists..., is vegetarian and uses microbial sources.
Dark gravies might also take advantage of caramel/caramelization/maillard products... which can be achieved by adding, well, caramel or something caramelized.