Heat the olive oil in a large pot over medium heat. Add the onion and cook until it softens, about 5 minutes. Stir in the garlic and cook for 1 minute more.
Add the sweet potatoes, black beans, vegetable broth, cumin, and chili powder. Bring the mixture to a boil, then reduce the heat and simmer uncovered for 20 minutes until the sweet potatoes are fork-tender.
Remove the pot from the heat. Stir in the lime juice. Use an immersion blender to partially blend the soup for a thicker texture, or leave it chunky if you prefer.
Ladle the soup into bowls. Top each serving with chopped cilantro and serve with lime wedges on the side.