Heat oil in a large saucepan over medium heat; cook and stir carrots, onion, and garlic until onion is softened, about 5 minutes. Stir chili powder and cumin into onion mixture; cook and stir until evenly coated, about 2 minutes.
Pour broth over onion mixture and add 1/2 of the black beans, corn, and black pepper. Bring broth mixture to a boil.
Blend tomatoes and remaining 1 1/2 cans black beans together in a food processor or blender until smooth; pour into broth mixture. Reduce heat to low, cover pot, and simmer until carrots are tender, 10 to 15 minutes.