Heat the olive oil in a large pot over medium heat. Add the diced onion and sauté for about 5 minutes, until translucent.
Stir in the minced garlic, diced carrot, and bell pepper. Cook for another 5 minutes until the vegetables are softened.
Add the drained black beans, vegetable broth, cumin, chili powder, smoked paprika, salt, and pepper. Bring the mixture to a boil.
Reduce the heat to low and let it simmer for about 20 minutes, allowing the flavors to meld.
For a creamier consistency, you can blend part of the soup using an immersion blender or transfer a portion to a traditional blender, then return it to the pot.
Stir in the lime juice just before serving.
Ladle the soup into bowls and garnish with fresh cilantro. Serve with a dollop of sour cream or Greek yogurt and tortilla chips, if desired.