Heat oil in a large soup pot over medium heat. Add the onion and carrots, and cook for 5 minutes until onion is soft and translucent. Stir in the garlic cloves, curry paste, coriander, cumin, and red pepper flakes to skillet. Cook, stirring occasionally, for 10 minutes.
Add in the broth and coconut milk and reduce heat to a simmer until carrots are soft, about 20 minutes. Season to taste, adding a pinch of salt or black pepper, if desired.
Remove the soup from heat and let cool slightly. Puree the soup until creamy and smooth using an immersion blender or blender. Depending on the size of your blender, you may need to work in batches. Return soup back to the pot and stir in the lime juice. Serve with chopped cilantro and extra coconut milk, for drizzle.
This nutritional information refers to each serving of the entire recipe and not just the products used as ingredients.