Rinse and sort through the black beans, removing any debris or damaged beans. In a large stockpot, combine beans with 8 cups of water and bring to a boil over high heat.

While beans are heating, dice the onions, bell peppers, and celery into small pieces. Mince the garlic cloves finely.

Once beans reach a boil, reduce heat to medium-low and simmer for 30 minutes until beans begin to soften.

Heat olive oil in a skillet over medium heat. Add onions, bell peppers, and celery, sautéing for 5-7 minutes until vegetables soften and onions become translucent.

Add minced garlic, cumin, oregano, black pepper, and bay leaves to the vegetables. Sauté for another 2 minutes until fragrant.

Transfer the sautéed vegetable mixture to the pot with the beans. Add salt and continue simmering for another 15-20 minutes until beans are completely tender.

Using an immersion blender, partially blend the soup to create a creamy texture while leaving some whole beans for texture. Alternatively, remove 2 cups of soup, blend it, and return it to the pot.

Stir in chopped cilantro and adjust seasoning with additional salt and pepper to taste.

Create 6 small wells in the simmering soup using a spoon. Carefully crack one egg into each well.

Cover the pot and let eggs poach in the soup for 4-5 minutes until whites are set but yolks remain slightly runny.

Serve immediately in deep bowls, ensuring each portion contains one poached egg. Garnish with additional fresh cilantro and serve with lime wedges and warm tortillas on the side.