Puree half of beans in a food processor or blender with 1 cup water until smooth.
Tie cilantro into a tight bundle with string.
Cook onion and garlic in olive oil in a 5-6 quart pot over moderate heat, stirring occasionally, until onion is softened but not browned, about 8 minutes.
Add tomato paste, vinegar, and 1 cup water, then bring to a boil and cook, stirring, 2 minutes.
Add pureed and whole beans, Italian frying pepper halves, cilantro, bay leaves, salt, oregano, pepper and remaining 2 cups water, then simmer, uncovered, stirring occasionally, 1 1/2 hours (mixture will reduce and thicken).
Remove and discard Italian pepper halves, cilantro, and bay leaves, then serve.