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1
Drain the soaked beans and cover with fresh cold water. Bring to a boil, then simmer until very tender — 60 to 90 minutes depending on age. Reserve all cooking liquid. The beans must yield completely to pressure between the fingers with no chalky centre.
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2
In a dry pan over medium heat, toast the plain flour, stirring constantly, until it turns a deep golden colour and smells nutty. Remove immediately from the heat. This is the tostatura della farina — a dry roux that gives the soup both body and depth.
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3
Warm the olive oil in a large, heavy pot. Add the smoked pork and sauté over moderate heat until it has rendered its fat and coloured at the edges. The smell should be fully smoky and the fat around the pork translucent.
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4
Add the rinsed sauerkraut to the pot and stir it through the rendered pork fat. Add the potato cubes, the cooked beans, and enough of the bean cooking liquid and water or light broth to cover generously. This is where the dish lives or dies: the acidity of the sauerkraut, the smoke of the pork, and the earthiness of the beans must enter a single long conversation — if the sauerkraut has been rinsed too thoroughly, the characteristic sourness is gone; if the pork is unsmoked, the dish is not jota.
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5
Whisk the toasted flour into a ladleful of hot broth from the pot to form a smooth slurry, then stir this back into the soup. Simmer the soup, partially covered, for 45 minutes. At the end, a spoon drawn across the surface should leave a brief, clearly defined channel before it closes.
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6
Taste and adjust the seasoning. The consistency should be thick enough to stand a spoon upright momentarily. Serve in deep bowls with a dash of olive oil poured at the table.