In a stockpot over low-med heat, cook the carrots and the onions in the peanut oil for 7 to 10 min.; cover and stir occasionally. You want the onions to brown but not burn, although if the burn a little bit it's not the end of the world. Add the garlic, curry, salt, and pepper; saute for 1 more minute Add the 3 cups broth, cover, and bring to a boil. Lower the heat and simmer for 10 to 12 min., or until the carrots are tender.
Add the coconut milk and bring to a low boil. Turn the heat off. Use a handheld blender to puree half of the soup; if you don't have one, then puree half the soup in a blender and add it back to the soup pot. Add the maple syrup and stir. Serve hot.