In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until translucent.
Stir in the minced garlic, grated ginger, and ground turmeric. Cook for an additional 2 minutes until fragrant.
Add the chopped carrots to the pot and pour in the vegetable broth. Bring to a boil, then reduce heat to a simmer. Cover and let cook for about 20 minutes, or until the carrots are tender.
Remove the pot from heat and use an immersion blender to puree the soup until smooth. Alternatively, carefully transfer the mixture in batches to a blender and blend until smooth.
Return the soup to low heat and stir in the coconut milk. Season with salt and black pepper. Allow the soup to heat through for about 5 more minutes.
Taste and adjust seasoning if necessary.
Notes
Serve in warm bowls, garnished with fresh cilantro and lime wedges.