This isn't, like, the height of delicious minestrone, but it's a serviceably tasty, eminently nutritious, and easily variable soup.
Stir fry some chopped onion (okay, is it cheating that I had some extra chopped onion in the fridge from the last time I cooked and so didn't have to spend time chopping?) in a couple tablespoons of heated olive oil until the onion is soft and just golden around the edges. If you really wanted, you could put in some chopped carrot and/or minced garlic as well, but for the twenty-minute stuff, I usually just use garlic powder.
Anyway, put in some pre-chopped (cheating again) tomatoes and tomato paste or just some canned chopped tomato or tomato puree and add water or broth to the desired dilution. Add the herbs and spices of your choice (salt, pepper, thyme, oregano, rosemary, marjoram, basil, bay, aforementioned garlic powder) and some pasta (I like fusilli). Cook until the pasta is almost done, then add some drained canned beans (I just added kidney) and some sort of green vegetable. By the time the pasta is done, the vegetable and beans will have heated through to proper tastiness.