Place 1 can black beans and chicken broth into a blender; cover and puree until smooth.
Heat a large saucepan, over medium-high heat; add chicken broth, onion, garlic and carrot; sauté until onion is tender and carrots are cooked; about 5 minutes.
Stir remaining 1 can black beans and liquid, tomatoes, yogurt, lime juice, cumin, red pepper flakes, and pureed beans into onion mixture; bring to a boil.
Reduce heat to low, cover, and simmer for 25 to 30 minutes, stirring occasionally.
Garnish with sour cream, cilantro, avocado and/or feta cheese, if using, to serve.
