In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté for 5 minutes until translucent.
Stir in the minced garlic and grated ginger, cooking for an additional 2 minutes until fragrant.
Add the diced sweet potatoes to the pot, stirring to combine. Cook for 3-4 minutes.
Sprinkle in the ground cumin, coriander, turmeric, salt, and pepper. Mix well, allowing the spices to coat the sweet potatoes.
Pour in the vegetable broth and bring the mixture to a boil. Once boiling, reduce the heat to low and let it simmer for 20-25 minutes until the sweet potatoes are tender.
Remove the pot from heat. Using an immersion blender, blend the soup until smooth and creamy. Alternatively, you can transfer the soup in batches to a regular blender, but be cautious with hot liquids.
Stir in the coconut milk and heat the soup gently for another 5 minutes. Adjust seasoning with salt and pepper as needed.
Serve hot, garnished with fresh cilantro or parsley and lime wedges on the side.