For our chili I started with olive oil, sauteed onion, celery, carrots, bell peppers, and garlic. I added cumin as the vegetables got a bit of brown to them, and then browned the beef with the vegetables. Tomato sauce, a small scoop of the vegetarian beans, chili powder, and some lime juice and water finished it off.
I made the same base for the beans, added the beans and the water and cooked till the beans were done. Don't add any acid or salt till the beans are done though. Beans cooked this way taste great on their own. I don't eat many beans for the same reason I avoid grains, but a few sometimes don't bother me. Once the beans were cooked through I added diced zuchini, tomato sauce, chili powder, lime juice, and salt and pepper.
I made all of the chili very mild and set out the rest of the very spicy pico de gallo for those that wanted some zip. Grated cheese, cilantro, and sour cream were also on the table along with the corn muffins.
Other aromatic bases that work well for soups or stews:
Coconut oil, with onion, galangal, turmeric, ginger, and either kefir lime zest or lemongrass. Add lime juice, fish sauce, and coconut milk.
Butter, leeks, celery, add cider vinegar and chicken stock.
Olive oil, onion, carrot, celery, bell pepper, herbs and tomato, add water or mild stock.
Olive oil, leek, fennel, fennel seed, orange zest, tomatoes, fish stock or clam juice.
You get the idea. And I always let some browning happen, in french cooking you often keep things pale, but the carmelization adds depth of flavor and a savory quality. When I was a vegetarian this browning step was the secret to good soups, and I still enjoy it even though meat stocks have so much more flavor. Sometimes I even make soup with water instead of stock just to keep the vegetable flavors front and center.
Once you have the aromatic base add your soup ingredients, meat, vegetable garnish, beans, what have you, and cook them till they are done.
Most soups or stews benefit from a taste as they are almost done and additional salt, pepper, an acid of some sort like citrus juice, tamarind paste, vinegar. I thicken bean and root vegetable soups by pureeing some. I add coconut cream, sour cream, or cream whenever appropriate. And I always add some fresh green herbs at the end.
Edited to add: my friend Theresa reminds me that I almost always added cheese to my vegetarian soups back in the day. Cheese is a wonder food if you ask me. It's also the main source of vitamin B12 in the American diet. If you want to add cheese to soup wait until it's in all other ways done and perfect, it helps if it's slightly thickened soup, pureed beans, potatoes, or even slightly thickened with corn starch. Then turn off the heat, wait for a few minutes and add your grated cheese gradually. If you re-heat your soup later do it gently so the cheese doesn't curdle.