In a food processor, combine the green pepper, onion and garlic. Pulse until finely chopped.
Add the olive oil to a large pot set over medium heat then add the chopped vegetables. Cook, stirring, until fragrant, about 3 minutes.
Stir in the black beans, bay leaf, ground oregano and 1 teaspoon kosher salt. Bring the mixture to a boil then reduce it to a simmer and cook, uncovered, for 10 minutes.
Stir in the white vinegar. Taste and season with salt and pepper, discard bay leaves then serve.