Cut the ½ of the sausage in half lengthwise, and then slice into 1/4- to 1/2-inch half moons.
Heat the oil a large saucepan over medium heat, and brown the sausage on both sides. Remove to a plate.
Pour the chicken broth into the pan, and stir to deglaze. Add the drained black beans, salsa, and cumin. Bring to a simmer and cook for 5 to 10 minutes. Remove approximately half the soup to a blender and blend until smooth. (The soup will be extremely hot, so please use caution when blending. You may also use an immersion blender to do this right in the saucepan.) Return the pureed soup to the pan along with the cooked sausage. Heat through, and enjoy with toppings of choice.