Dice the onion and saute until soft and translucent (about 5 minutes.)
Once the onions are soft, add the curry paste and continue to saute for a little longer (about a minute) to wake up the spices. (4 Tablespoons sounds like a lot, but it's not very spicy given the batch size of the soup.)
Peel and dice sweet potato. Slice carrots. Add to the pot along with ~3 cups of broth or water.
Simmer for about 30 minutes, until the vegetables are extremely tender.
Turn off the heat. Let the soup cool just a little so it is safer to blend. Add the coconut milk (if yu want to get fancy, you can reserve a little to drizzle on later as a garnish.)
Blend the soup in batches. Reheat and serve.
You can also just add whatever spice you want instead of curry paste. Also, it's good with extra ginger.