This is not any particular kind of soup. This is just Soup- basically, a meat and vegetable dish in a tasty broth, with things like noodles, rice, dumplings, etc. optional. Change it out, use what you have and/or what you like.
Start with a rich broth. This can be the broth from a pot roast or corned beef boiled dinner (but with the corned beef, dilute well if it’s too salty!), or a purpose-made stock from poultry bones and carcasses, or one made from a nice ham bone.
Stock- make the day before
If you’re making the stock, take the bones from a poultry roast- after stripping the meat from it and reserving it for the soup- and break them up. Roast them at 400F for an hour or so, along with coarsely cut celery, onions, and carrots, and a couple of cloves of garlic. Stir every 20 min or so. Go longer if you have to- you want a deep brown caramelization.
Put bones and roasted veg into a large pot. Add seasonings if you like- a bay leaf or 2 and some peppercorns are good. Deglaze roasting pan with a half cup-1 cup of wine- white usually- until you have dissolved all the fond and boiled off the alcohol. Add to pot with veg and bones. Add water to cover, and simmer for hours- at least 2-4, and more is not a problem. Strain stock and discard bones and played-out veg.
Ham is different. Take a meaty ham bone and simmer, with bay leaf and peppercorns, until the connective tissues have melted. Remove, cool, and pull meat off bones. Discard bones and chop up meat.
If your stock has a LOT of fat, refrigerate it overnight, or put it on the porch in the winter, then pull off most of the hardened fat. You really do want to leave some fat- it helps both the flavor and the “fillingness” a LOT.
Now it’s time to craft the soup. I always include onions, carrots, and potatoes (usually gold or red). More celery is possible. Sweet potatoes break down and thicken and enrich the broth- I especially like them in our annual goose soup. Turnips and/or parsnips are great in most soups. Ham-based ones, to my mind, require legumes- split peas are easy, and beans are good. The trick here is sequencing. If you are adding dried beans, add them first and let them get mostly cooked before adding anything else. If you are adding brown rice, add it with the tougher veg- carrots and celery. Basically, move from the stuff that takes more cooking to the stuff that requires less. Potatoes are in the middle, and turnips and parsnips toward the end. The chopped meat is added right before serving the first day.
(Ham soup, for us, usually has beans or split peas, carrots, celery if we have it, onions, and potatoes; corned beef has carrots, onions, potatoes, turnips; goose has sweet potatoes, carrots, onions, potatoes, turnips, maybe parsnips; etc.)
If you are wanting noodles, I strongly suggest cooking them separately and adding them to the bowls right before serving. If dumplings, cook in the pot but remove and reheat them separately- else the whole thing becomes a porridge. Tasty, but not great-looking.
You can always add more water to soup, for texture or quantity.
If you are not happy with your soup, think about what’s missing. For several years I was not pleased with mine because I thoroughly de-fatted it, which is a Bad Idea; even if you forswear fat, leave a tablespoon or 2 for a batch of soup. It may also need salt. I often add a pinch of salt to the veg before roasting them, and that suffices- but we tend to eat pretty low-salt, and you might want more, especially with poultry soup rather than ham or corned beef.
This generally makes at least 6-8 servings. Lots of good veg, “bone broth”, and very frugal. And delicious!