1. Drain the beans through a strainer set over a bowl. Transfer to a large, heavy soup pot or Dutch oven. Measure the liquid in the bowl and add enough water to measure 2 quarts. Add to the beans and bring to a gentle boil over medium heat. Cover, reduce the heat to low and simmer 1 hour. Add salt to taste and the bouquet garni, and continue to simmer until tender but intact, about 30 minutes.
2. Meanwhile, heat the olive oil over medium heat in a large, heavy frying pan and add the onion. Cook, stirring, until the onion is tender, about 5 minutes, and add the paprika. Stir together for about a minute, and add the garlic and a pinch of salt. Cook, stirring, for a minute or two, until the garlic and onions are very fragrant, and stir in the tomatoes. Cook, stirring often, until the tomatoes are cooked down and fragrant, about 5 to 10 minutes. Add a ladleful of broth from the beans and stir to deglaze the bottom of the pan.
3. Stir the onion mixture into the beans. Add salt and pepper to taste. Add the winter squash and lima beans. Cover and simmer for about 30 minutes, until the squash and all the beans are tender. Taste and adjust salt, and add freshly ground pepper. Remove the bouquet garni. Just before serving stir in the fresh basil. Serve in wide soup bowls, passing Parmesan for sprinkling.