Add 1 can white beans in sauce and chicken broth to blender; puree until very smooth, about 1 minute; set aside.
Heat oil in medium pot over medium-high heat. Add chorizo. Cook, stirring occasionally, until golden brown, about 5 minutes. Using slotted spoon, transfer chorizo to paper towel-lined plate; set aside. Add remaining can white beans in sauce and reserved white bean puree to pot; bring bean mixture to boil. Reduce heat to low. Simmer, stirring occasionally, until soup thickens, about 5 minutes.
Stir 2 tbsp. cilantro and most of reserved chorizo into pot; evenly divide soup among serving bowls. Garnish with remaining cilantro and chorizo. Drizzle with olive oil; serve.