Place leeks, potatoes, and carrots in a large pot. Pour over the broth and water.
Bring to a boil then reduce to a simmer. Cook and stir occasionally until vegetables are tender, 20-30 minutes depending on size.
Remove from heat and stir in coconut milk.
Season to taste with your preferred salt blend and cayenne pepper sauce. Serve warm.
**For a less-chunky soup, use an immersion blender or regular blender to bring it to your desired texture.