Heat the olive oil or butter in a large pot or Dutch oven over medium-high heat. Add the chorizo sausage and cook, stirring occasionally, until lightly browned around the edges. Remove into separate bowl.
Add the onion, season with ½ teaspoon salt and cook, stirring occasionally, until soft and slightly browned, about 5 minutes.
Add the garlic and cook, stirring, 1 minute.
Add the potatoes, ½ teaspoon salt and a few grinds of pepper. Cook, stirring occasionally, until well coated, about 3 more minutes.
Add the chicken broth, bay leaves and paprika. Add the sausage back in. Bring to a simmer, then reduce the heat to medium and cook 12 minutes.
Add the chard; cover and cook, stirring, until the potatoes are tender and the chard is wilted, 15 more minutes. Season with salt and pepper.
Ladle into bowls; top with parsley, drizzle with olive oil and serve with bread.