Heat the olive oil in a large pot over medium heat. Add the diced onion and cook for 3 minutes until it softens.
Stir in the minced garlic and curry powder. Cook for 1 minute until the spices smell fragrant.
Add the sweet potato cubes and vegetable broth. Bring the mixture to a boil, then reduce to a simmer and cook for 15 minutes until the sweet potatoes are tender when pierced with a fork.
Remove the pot from the heat. Stir in the coconut milk along with the salt and black pepper.
Use an immersion blender to puree the soup until smooth. If you prefer a chunkier texture, mash some of the sweet potatoes with a potato masher instead.
Ladle the soup into bowls. Top each serving with chopped cilantro and serve with lime wedges on the side.