Put black beans, quartered green pepper, and bay leaves in a large saucepan; add 8 cups of water. Bring to a boil over medium-high.
Reduce heat to low, partially cover saucepan, and cook, stirring occasionally, until beans are tender, about 2 ½ hours. Remove and discard green pepper pieces and bay leaves.
Meanwhile, heat 2 tablespoons olive oil in a large skillet. Add minced bell peppers and onion; cook over medium until softened, 6 to 10 minutes. Stir in cumin, oregano, and tomato paste.
Cook garlic in remaining ½ cup of olive oil in a small saucepan over medium-low until golden brown.
When beans are tender, add sautéed pepper mixture and garlic in its oil. Season with salt and simmer gently for 5 minutes to blend flavors.
Cover and refrigerate overnight or for up to 3 days. Reheat gently before serving.
