If using dried beans, soak them in water overnight. In the morning, drain, rinse well, and boil in unsalted water until tender, changing the water 2-3 times while they cook.
Heat the coconut oil in a large pot over low heat. Slice half the carrot thinly and grate the other half on a coarse grater; add both to the pot and stew gently.
Grate the Jerusalem artichoke on a coarse grater and add it to the carrots; keep stewing until slightly softened. (Or use 2 extra potatoes instead and skip this step.)
Peel the potatoes and cut into small cubes. When the carrot and Jerusalem artichoke have softened a little, add the potatoes and pour in 8 ½ cups (2 L) water. Cook for about 7 minutes, until the potatoes are ready.
Add the beans, salt, spices, chopped sorrel, and greens. Cook for 2 minutes, then turn off the heat.
Let the soup infuse for at least 5-10 minutes, then serve.