Place a large saucepan over medium-high heat with 1 turn of the pan of EVOO, about 1 tablespoon. Add the chorizo to the pan and cook until crispy, 4-5 minutes. Remove from pan and reserve.
Add the onion, garlic, serrano, paprika, some salt and pepper to the pan, and cook until the onions are tender, 5-6 minutes. Add the black beans and chicken stock to the pan, and bring the liquids up to a bubble.
Ladle a couple of scoops of the soup into the bowl of a food processor and process until smooth. Return the pureed soup to the pot and keep warm.
After pureeing the beans, rinse the food processor bowl out and return it to the base. Remove the pit from the avocados and scoop them out into the bowl along with the sour cream, lime zest and juice, and process until smooth.
Serve the soup topped with some avocado cream and reserved crispy chorizo.