Thoroughly mash black beans in a small bowl. Stir salsa into the beans; transfer mixture to a small saucepan and place over medium heat. Pour vegetable broth into the saucepan; stir. Bring the liquid to a simmer and cook until the liquid reduces slightly and thickens to your preferred texture, 10 to 15 minutes.
Season the soup with salt. Sprinkle Cheddar cheese over the soup and stir to melt. Continue to cook until heated through, 1 to 2 minutes more. Divide between 2 bowls and top each portion with a dollop of sour cream.