01 - Warm the olive oil in a large soup pot over medium heat. Add the chorizo and sauté for 3 to 4 minutes, stirring regularly until it is browned and the oil is colored. Remove about half the chorizo with a slotted spoon and reserve for garnish.
02 - Add chopped onion, minced garlic, and sliced leeks to the pot. Cook for 5 minutes, stirring occasionally, until vegetables are softened but not caramelized.
03 - Incorporate diced potatoes and smoked paprika into the mixture. Sauté for an additional 2 minutes.
04 - Pour in the stock and bring contents to a boil. Reduce heat to low and simmer for 20 minutes, until potatoes are thoroughly tender.
05 - Using a stick blender, partially blend the soup in the pot to achieve a creamy consistency while leaving some chunks for texture. Alternatively, transfer half the soup to a countertop blender, blend, and return to the pot.
06 - Stir in heavy cream if using, return reserved chorizo to the pot, and adjust seasoning with salt and black pepper. Warm through for 2 to 3 minutes.
07 - Ladle the soup into serving bowls, finish with chopped parsley, and accompany with crusty bread if desired.