Caldo verde is the soup Portugal eats at 2 in the morning after a wedding, at noon in a roadside café in the Minho and, in my kitchen, on the first evening the radiators come on. It is a potato soup, thick with onion and thinned with water, into which a tangle of dark greens is dropped at the last minute. Its genius is in the cutting: the kale, or in Portugal a loose-leaf cabbage called couve galega, is rolled tight and sliced into threads so fine that they cook in two minutes and float in the broth like grass. A slice of chouriço on top is traditional. A heavy pour of good olive oil is mandatory.

Ingredients, for 6: 800 grams floury potatoes, peeled and cut into chunks; 1 large onion, roughly chopped; 2 cloves garlic, sliced; 80 milliliters olive oil, plus more to finish; 1.5 liters water; 1 teaspoon fine salt, plus more to taste; 250 grams Tuscan kale, collard greens or Portuguese cabbage, tough stems removed; 120 grams chouriço or Spanish chorizo, sliced into thin rounds; black pepper.

Make the base. Warm half the olive oil in a large pot over medium heat and add the onion and garlic with a pinch of salt. Cook gently for 8 minutes, until soft and translucent but not browned. Add the potatoes, the water and the teaspoon of salt, bring to a boil, then lower to a simmer and cook, partly covered, until the potatoes fall apart when pressed, about 25 minutes.

Cut the greens. While the potatoes cook, stack the leaves a few at a time, roll them into a tight cigar, and with your sharpest knife slice across the roll as thinly as you can, a millimeter or two. Fluff the threads apart with your fingers. This is the step that makes the soup; wide ribbons will be chewy and will not float.

Blend and finish. When the potatoes are done, blend the soup with a stick blender until it is smooth and the consistency of thin cream, adding a splash of hot water if it is too thick. Taste for salt; it should be well seasoned, because the greens will dilute it. Return to a simmer, add the remaining olive oil, then drop in the sliced greens and cook, uncovered, for 2 to 3 minutes, just until they are tender and still bright. Do not cook longer; the soup should be green, not khaki.

Meanwhile, if using the chouriço, fry the rounds in a dry pan over medium heat for a minute a side until the edges crisp and the fat runs. Ladle the soup into bowls, lay a few slices of sausage on each, grind over black pepper and finish with a generous thread of olive oil. Serve with broa, the dense Portuguese cornbread, or any coarse bread. The soup keeps for three days, though the greens will darken; it is better to make the base ahead and add fresh greens when reheating.