Heat olive oil in a large pot over medium heat. Add onion, garlic, carrot, and bell pepper. Cook until vegetables are tender, about 5-7 minutes.
Add black beans, vegetable broth, cumin, chili powder, paprika, salt, and black pepper. Stir to combine.
Bring to a boil, then reduce heat and simmer for 20 minutes.
Use a blender to puree the soup until smooth, or leave it chunky if you prefer.
Stir in diced tomatoes and lime juice. Simmer for an additional 5 minutes.
Serve hot, garnished with chopped cilantro.