In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and sliced chorizo. Cook for another 5 minutes until the chorizo is browned and fragrant.
Add the diced potatoes, chicken broth, smoked paprika, cumin, salt, and pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for 20-25 minutes, or until the potatoes are tender.
Once the potatoes are cooked, use an immersion blender to puree the soup until smooth. If you prefer a chunkier texture, blend only half of the soup and leave the rest as is.
Stir in the heavy cream and heat through for an additional 5 minutes. Adjust seasoning if necessary.
Serve hot, garnished with fresh parsley.