Heat olive oil in a medium stockpot set over medium-low heat. Add onions, garlic, and bell peppers; cook until onions are soft but still translucent, about 25 minutes.
Add black beans, black-bean puree, bay leaves, cumin, and oregano. Season with salt and black pepper; stir.
Cook mixture until thickened, about 10 minutes. Stir in vinegar and cilantro. Garnish with more cilantro and the red pepper, if desired.