Heat olive oil in a large pot over medium heat. Add onion, garlic, carrots, celery, bell pepper, and jalapeño. Cook until softened, about 8 minutes.
Stir in cumin, smoked paprika, and oregano; cook for 1 minute until fragrant.
Add soaked black beans, broth (or water), and bay leaves. Bring to a boil, then reduce heat to low, cover, and simmer for 1.5 to 2 hours, until beans are tender.
Remove bay leaves. Using an immersion blender, partially blend the soup to your desired consistency (or transfer 2 cups to a blender and blend, then return to pot).
Stir in lime juice, and season with salt and pepper to taste. Simmer for 5 more minutes.
Serve hot with desired toppings.
Tips
To save time, use three 15-ounce cans of black beans, drained and rinsed. Reduce broth to 4 cups and simmer for 20 minutes.
Soup thickens as it cools; thin with extra broth when reheating.
Store leftovers in the refrigerator for up to 5 days or freeze for up to 3 months.