Heat the olive oil in a large pot over medium heat. Add the onion and cook until it softens, about 5 minutes.
Stir in the garlic, chipotle peppers, and adobo sauce. Cook for 1 minute until fragrant.
Add the cumin and smoked paprika. Stir for 30 seconds to toast the spices.
Pour in the black beans and vegetable broth. Add the salt and bring the mixture to a simmer.
Cook uncovered for 15 minutes, stirring occasionally. Use an immersion blender to partially blend the soup, leaving some beans whole for texture.
Stir in the lime juice. Taste and adjust salt if needed. Serve hot with chopped cilantro on top.