Heat the olive oil in a large pot over medium heat and sauté the onion and pepper until softened, about 5 minutes.
Add in the water, potatoes, corn, thyme, cayenne, salt, and black pepper. Bring the water to a boil, then cover and lower the heat, simmering until the potatoes are fork-tender, about 25 to 30 minutes.
When the soup is done cooking, stir in the coconut milk. Use a ladle to scoop half of the soup into a blender, and carefully blend until smooth. (When blending hot liquids, be sure to lightly cover the vent in the lid with a thin dish towel, so steam can escape and you won't get splattered with hot soup.)
Pour the blended soup back into the pot, and then adjust the seasoning to taste. Serve warm with any toppings you love. Leftover soup can be stored in an airtight container in the fridge for up to 5 days.
This recipe was updated in May 2021. If you prefer the original recipe, simply omit the coconut milk and cayenne pepper. I think this updated version is even better, though!Nutrition information is for 1 of 4 servings. This information is automatically calculated and is just an estimate, not a guarantee.See substitution notes in this post if you need swap ideas!