Heat 3 tablespoons olive oil in a large pot over medium heat.
Add diced onion (and carrots/celery if using) and sauté until softened, about 5–7 minutes.
Stir in minced garlic and jalapeño and cook 1 minute until fragrant.
Add ground cumin, smoked paprika, and oregano; toast the spices for 30–60 seconds.
Stir in tomato paste (if using) and cook 1 minute to deepen flavor.
Add drained black beans and pour in 4 cups broth; add the bay leaf and bring to a simmer.
Reduce heat and simmer gently for 15–20 minutes to let flavors meld.
Remove the bay leaf, then blend about half the soup with an immersion blender or in batches in a regular blender until smooth.
Return blended soup to the pot, stir, and adjust thickness with more broth if needed.
Season with salt, pepper, and lime juice; simmer 2–3 minutes to meld flavors.
Ladle into bowls and garnish with cilantro, diced avocado, sour cream or yogurt, and a drizzle of olive oil before serving.