Gather all ingredients and dice the potatoes and onion. Mince the garlic and chop the kale or spinach. Set aside.

In a large pot or Dutch oven, heat olive oil over medium heat. Add the chorizo and cook until browned and fully cooked, about 5-7 minutes. Break it up into smaller pieces as it cooks. Remove the chorizo from the pot and set aside, leaving the rendered fat in the pot.

In the same pot, add the diced onion and sauté for about 3-4 minutes until it’s translucent. Add the minced garlic and sauté for an additional minute until fragrant.

Stir in the diced potatoes and smoked paprika, mixing well. Pour in the chicken or vegetable broth, bringing the mixture to a rolling boil. Reduce the heat to a simmer and cook for about 15-20 minutes, or until the potatoes are tender.

Once the potatoes are cooked, use an immersion blender to puree the soup until smooth. Alternatively, transfer the soup in batches to a regular blender and blend until smooth. If desired, leave some chunks of potatoes for texture.

Return the pureed soup to low heat and stir in the heavy cream and milk. Add the chopped kale or spinach. Let the soup simmer gently for about 5 more minutes, allowing the greens to wilt. Season with salt and pepper to taste.

Stir the cooked chorizo back into the soup, heating through for another 2-3 minutes.

Ladle the hot soup into bowls and garnish with fresh parsley or cilantro. Serve with crusty bread if desired.