Heat the oil in a large high-sided skillet or Dutch oven over medium-high heat. Add the onion, celery and bell pepper and cook, stirring, until they begin to soften, 4 to 5 minutes. Add the chipotle pepper, chili powder and ground cumin and cook, stirring, for an additional 30 seconds. Add the vegetable broth, black beans and diced tomatoes. Bring the mixture to a simmer, reduce the heat to medium and cook for about 15 minutes.
Add the lime zest and juice and season with salt and pepper to taste.
Use a spoon to create 4 small wells in the soup. Crack each egg into a small bowl and carefully drop one egg into each of the wells. Cover and cook until the eggs are set to your liking, about 5 minutes. Top with the fresh cilantro and scoop 1 egg into each of 4 bowls, then divide the rest of the soup among the bowls and serve.