Prepare the Beans (if using dried):
If using dried black beans, rinse them thoroughly and soak them overnight in water. Alternatively, you can use the quick-soak method: bring the beans to a boil in a pot with water, then remove from heat and let them sit covered for 1 hour. Drain before using.

Sauté the Aromatics:
In a large pot, heat the olive oil over medium heat. Add the chopped onion and cook until soft and translucent, about 5 minutes. Add the minced garlic, bell pepper, and diced carrot. Cook for another 3-4 minutes until the vegetables begin to soften.

Cook the Soup:
Add the soaked (or canned) black beans, diced tomatoes, vegetable broth, cumin, smoked paprika, and bay leaf to the pot. Bring the soup to a boil, then reduce the heat and simmer for 30-40 minutes (or 20 minutes if using canned beans), or until the beans are tender and the flavors have melded together.

Blend the Soup:
Once the beans are tender, remove the bay leaf. For a smoother texture, use an immersion blender to blend the soup directly in the pot until it reaches your desired consistency. Alternatively, you can blend the soup in batches in a regular blender. If you prefer a chunkier texture, blend only part of the soup.

Season and Finish:
Stir in the lime juice, and season the soup with salt and pepper to taste. For extra flavor, add more cumin or smoked paprika if desired.

Serve and Garnish:
Ladle the soup into bowls and garnish with fresh cilantro. Serve with a side of crusty bread or over rice for a more filling meal.