Dice the pepper, peel and dice the carrot, and mince the red onion and cilantro.
In a soup pot over medium heat, heat the olive oil. Add in the pepper, carrot and red onion, and sauté until the veggies are mostly tender (around 7 minutes).
Meanwhile, peel the skins off the potatoes, then dice them.
Once the veggies are tender, add in the broth, salsa, cilantro, black beans, potatoes and spices. Squeeze the juice of the lime into the pot. Cover, bring to a boil, then lowly simmer until the potatoes are tender, around 15 minutes.
Use an immersion blender to process the soup until mostly smooth. If you don't have an immersion blender, transfer the soup to a blender or food processor to blend until mostly smooth, then return to the pot.
If soup isn't at desired consistency yet, cook for a few more minutes. Otherwise, immediately ladle the soup into bowls, then enjoy with your favorite toppings.