Heat oil in a skillet over medium heat; stir in carrots, onion, celery, and garlic. Saute until the onion has softened and turned translucent, about 5 minutes. Add chicken stock, bay leaves, salt, pepper, and Cajun seasoning. Bring to a simmer and cook until vegetables are tender, about 20 minutes. Remove bay leaves.

Puree soup with an immersion blender until smooth. Reduce heat to low, add white beans and chorizo sausage, and heat for another 10 minutes.