Put the black beans, quartered green pepper and bay leaves in a large saucepan add 8 cups of water. Bring to a boil over moderately high heat. Reduce the heat to low, partially cover the saucepan and cook, stirring occasionally, until the beans are tender, about 2 ½ hours. Remove and discard the green pieces and bay leaves.
Meanwhile, heat 2 tablespoons of the olive oil in a large skillet. Add the reserved sofrito from the first recipe and warm through. Stir in the cumin, oregano and tomato paste. Cook for a couple of minutes to cook the raw flavor off of the tomato paste.
When the beans are tender, add the sofrito mixture, season with salt and simmer gently for 5 minutes to blend the flavors.