Heat the olive oil in a large pot over medium heat. Add the diced onion and cook for 4 minutes until it softens.
Stir in the minced garlic and cook for 1 minute until fragrant.
Add the diced sweet potatoes along with the cumin, smoked paprika, and cayenne pepper. Stir to coat the potatoes evenly with the spices.
Pour in the vegetable broth and bring the mixture to a boil. Reduce the heat to a simmer, cover the pot, and cook for 15 minutes until the sweet potatoes are tender.
Add the chickpeas and continue to simmer for 5 more minutes. Season with salt and black pepper.
Use an immersion blender to partially blend the soup, leaving some chunks for texture. Stir in the chopped cilantro just before serving with lime wedges on the side.