Sauté Aromatics: In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 3-4 minutes. Add the garlic and ginger, and cook for another minute until fragrant.
Add Curry Paste: Stir in the Thai red curry paste and cook for another 1-2 minutes, allowing the flavors to meld.
Cook Vegetables: Add the diced sweet potatoes, carrots, and vegetable broth. Bring to a boil, then reduce heat and simmer for about 15 minutes, or until the vegetables are tender.
Blend the Soup: Remove the pot from the heat. Using an immersion blender, blend the soup until smooth. (Alternatively, you can carefully transfer the soup in batches to an upright blender and blend until smooth. Be sure to let the soup cool slightly and blend with the lid slightly ajar to allow steam to escape.)
Finish with Coconut Milk: Return the pot to low heat and stir in the coconut milk. Season with salt and pepper to taste, and add the lime juice.
Serve and Garnish: Ladle the soup into bowls and garnish with fresh cilantro, lime wedges, chopped peanuts, and red chili flakes if desired.