Sauté Aromatics: Heat olive oil in a large pot or Dutch oven over medium heat. Add onion and bell pepper; cook, stirring occasionally, until softened, about 5-7 minutes.
Add Spices: Stir in garlic, jalapeño (if using), cumin, oregano, and cayenne pepper (if using). Cook for 1 minute more, until fragrant.
Combine Ingredients: Add the rinsed black beans, vegetable broth, diced tomatoes, and bay leaf to the pot. Stir to combine.
Simmer Soup: Bring the mixture to a simmer, then reduce heat to low, cover, and cook for at least 20 minutes, allowing flavors to meld.
Blend for Texture: Remove the bay leaf. Using an immersion blender, carefully blend a portion of the soup directly in the pot until desired thickness and smoothness are achieved, leaving some beans whole for texture. Alternatively, transfer 2 cups of soup to a blender, blend until smooth, and return to the pot.
Season and Serve: Season the Black Bean Soup with salt and freshly ground black pepper to taste. Stir in fresh lime juice before serving. Ladle into bowls and garnish with fresh cilantro.