Stir crumbles, 1 can great Northern beans, vegetable broth, salsa, and corn together in a large pot over low heat.
Puree remaining can great Northern beans in a blender until smooth; stir with the mixture in the pot. Bring the mixture to a simmer and cook for 30 minutes.
Stir jalapeno pepper Cheddar cheese and Cheddar cheese into the chili; cook, stirring frequently, until the cheese is melted, 5 to 10 minutes more.
