Heat oil in a Dutch oven or large soup pot over medium-high heat. Once hot, add the onions and carrots; cook until the veggies start to soften, around 8 minutes.
Stir in the tomato paste, curry paste, garlic, and ginger. Cook for 3 to 4 minutes, stirring occasionally, until the tomato paste turns brick red and starts sticking to the pan. Add salt and pumpkin spice.
Add pumpkin puree and broth; stir well to combine. Use a wooden spoon to release any browned bits stuck to the bottom of the pan. Bring soup to a boil, reduce heat and simmer for 15 minutes.
Carefully transfer the soup to a high power blender using a ladle. Remove center piece of blender lid (to allow steam to escape), and secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid splatters), and blend until smooth. (Alternatively, you can use an immersion blender and blend the soup right in the pot!)
Pour blended soup back into pot and stir in coconut milk. If needed, reheat for another 1 to 2 minutes, though the soup should still be quite hot. Stir in lime juice, ladle soup into bowls, and add garnishes of choice.
TO STORE: Store cooked pumpkin soup in an airtight storage container for up to 1 week in the refrigerator.TO REHEAT: For best results, reheat soup in a small saucepan over medium heat, stirring often, until heated through. You can also reheat in the microwave, however it requires frequent stopping and stirring. Otherwise, you end up with soup that's scorching on the top, and barely heated through on the bottom.TO FREEZE: Let soup cool until it's close to room temperature before transferring to an airtight container or freezer-safe gallon ziptop bag. Store in the freezer for up to 3 months. Let thaw overnight in the refrigerator before reheating.