Heat coconut oil in a large pot over medium heat. Add onion and cook until starting to brown (4-5 minutes).
Add curry paste and garlic and sauté 1 minute longer. Add carrots and broth and bring to a boil. Reduce heat to a simmer and cook for 20 - 25 minutes until carrots are soft.
Use an emersion blender (or transfer to a food processor or blender) and blend until smooth. Add coconut milk, salt, and lime juice (return to pan first if using a food processor or blender) and heat to a simmer. Let simmer for 5 minutes to let flavors meld.
Ladle soup into bowls and garnish with cilantro, roasted peanuts, lime wedges, and crushed red pepper flakes.
Notes
* I use that I buy at the Asian superstore, but they sell it on Amazon too.