Heat olive oil in a large pot or Dutch oven over medium heat. Add the onion, celery, carrot, salt, and several grinds of pepper. Cook for 10 to 15 minutes, stirring occasionally, until the veggies are soft.
Add garlic, cumin, coriander, and chili powder. Stir for 30 seconds to release their aromas.
Stir in the black beans (with their liquid), chipotle peppers, adobo sauce, and vegetable broth. Bring the soup to a gentle simmer and cook for 30 minutes.
Allow the soup to cool slightly. Transfer half to a blender and puree until smooth, then return it to the pot. Alternatively, use an immersion blender directly in the pot to blend until the desired consistency is reached.
Stir in fresh lime juice and taste. Adjust seasonings as needed. Serve with lime wedges and desired toppings.