In large saucepan, heat oil over medium-high heat. Add carrot, onion, garlic, and cumin. Saute until lightly softened, about 5 to 7 minutes.
Stir in black beans, with liquid, and broth. Heat to boiling; reduce heat to medium-low, and simmer 10 minutes. Remove from heat; cool 5 minutes.
Puree soup in blender in small batches. Return to saucepan to reheat, and stir in lime juice. Divide among bowls and top with sour cream and cilantro, if desired.