Soup is the most forgiving thing in cooking and the best use for vegetables that are past their best but not past saving. There is no recipe to learn — there is a shape, and once you can see it you can make soup out of nearly anything in the drawer.
The shape
Fat, then onion, then the vegetable, then liquid, then blend or not. That is the whole thing. In practice: a spoon of oil or butter, a chopped onion cooked slowly until soft, garlic for the last minute, whatever vegetables you have cut small, then enough stock or water to just cover. Simmer until the vegetables give way to a spoon, which is between ten and thirty minutes depending on what they are.
Cover, do not drown
The commonest mistake is too much liquid. Add enough to just cover the vegetables — you can always loosen a thick soup, but you cannot easily take water back out of a thin one. If you have no stock, water and a properly cooked onion make a better soup than a stock cube dissolved into a pot of nothing. A parmesan rind, a spoon of miso or a splash of soy will also give water a backbone.
One starchy thing keeps it from tasting thin
A potato, a handful of rice, a slice of bread or half a tin of beans blended in gives body without cream. This is why so many classic soups contain a potato that nobody can taste. If it is still thin after blending, simmer it uncovered for a few minutes rather than adding flour. Evaporation concentrates flavour; flour only thickens.
Blend, or deliberately do not
Blending makes it feel like a made thing rather than boiled vegetables, and it hides a multitude of odd shapes. Blend it hot, in batches, with the lid vented. Or leave it chunky and add something that gives every spoonful a second texture: beans, torn bread, pasta, shredded greens added at the end.
Finish it properly, and it stops being leftovers
Every soup wants three things at the end: acid, fat and something on top. A squeeze of lemon or a drop of vinegar, a swirl of oil, cream or yoghurt, and something with crunch — croutons, toasted seeds, crisp onions, a hard cheese. Without those it tastes like a soft, warm bowl of nothing. With them, the same pot tastes like it was intended.
Onion in fat, vegetables, just enough liquid, one starchy thing, then acid, fat and crunch at the end. That is soup — and it happens to be the most reliable way to eat everything in the vegetable drawer before it goes.