Heat the olive oil in a large, lidded pot like a Dutch oven over medium-high heat. When it's hot, sauté the onions until they just start to brown a little. Stir in the garlic and cook another minute.

Add the quail, stock, vinegar, parsley stems, celery stalk, and thyme and bring to a simmer. Add salt to taste. Cover the pot and simmer very gently until the quail are tender, about 1 to 2 hours depending on whether the quail are farmed or wild.

While that's happening, bring a large pot of water to a boil and add salt. This is your pasta water, and you want this ready when the quail are.

When the quail are tender, gently move them from the pot to a plate to rest. Strain the broth into another pot, or a bowl (then wipe out the original pot), and fish out the thyme, celery and parsley stems.

Cook the angel hair pasta in the salted water for a minute or three, then move some to each person's bowl. Pour the broth over, and, if you want, chop the leaves from the parsley as a garnish.

Serve the quails on the onions, topped with paprika and black pepper. If they've cooled too much, pour just a little of the hot broth over them before adding the pepper and paprika.