Dice the onions, carrots, celery, and bell peppers. Finely dice the garlic and de-seeded chilies.
Pick the leaves off the cilantro and reserve for the salsa. Finely chop the cilantro stalks.
Over a medium heat, add 3 tablespoons of water to a large saucepan. Add the onions, carrots, celery, bell peppers, garlic, red chilies, coriander stalks, bay leaf, oregano, black pepper, and sea salt. Stir to combine, place a lid on the saucepan and sweat the vegetables for 10 minutes, stirring occasionally.
Drain the black beans, rinse well, and add to the saucepan with the boiling water. Stir to combine. Replace the lid and reduce heat so the soup simmers and cooks for 30 minutes (60 minutes if using dried, soaked black beans).
Just before the soup is done, prepare the lime salsa. Finely chop the reserved cilantro leaves, tomato, and salad onion. Add the lime juice, stir, and lightly season to taste.
Serve the soup in bowls and top with the lime salsa.