In a large pot over medium heat, warm the 1/4 cup extra-virgin olive oil. Add the 10 ounces chouriço, linguiça, or Spanish chorizo and cook until lightly browned on both sides, 3 to 5 minutes. Remove the sausage slices with a slotted spoon and transfer them to a plate, making sure they drain well into the pot; its fat will flavor the soup.
Dump the 1 large Spanish onion into the pot. Sprinkle with kosher salt and cook, stirring occasionally, until softened and translucent, 5 to 7 minutes. Add the 2 garlic cloves and cook for 2 minutes more.
Plonk in the 6 medium potatoes, add the 8 cups cold water (or a combo of water and chicken stock), and bring to a boil. Reduce the heat to a simmer. Cook until the potatoes are almost tender, 10 to 20 minutes. Remove from the heat and let the soup cool slightly.
When the caldo verde has cooled a little, purée it using an immersion blender or a food processor. (Tradition demands that one slice—and only one slice—of chouriço is added to each bowl, lthough some cooks like to add half the sausage to the soup before puréeing. It’s your choice. And that one-slice thing? To hell with it!)
Add the 1 pound collard greens or kale to the soup, bring it back to a boil, and then reduce the heat and simmer until tender, 2 to 5 minutes. Season with more salt, if needed, and freshly ground black or white pepper.
Ladle the caldo verde into bowls and garnish with the remaining slices of chouriço. Comer agora!