Heat butter in a large pot over medium-high heat. Add leeks and onion, reduce the heat to medium, then cook, stirring occasionally, until softened. Add chopped garlic, then cook.
Pour in chicken or vegetable stock, then add the cubed potatoes, curry powder, and sweet paprika. Bring to a boil, then reduce the heat to a simmer and cook until the potatoes are tender.
Use an immersion blender to purée until very smooth. See note below for instructions using a traditional blender.
Season the soup with Kosher salt and freshly ground black pepper, then stir in coconut milk or heavy cream. Taste and adjust seasoning, as needed. Serve immediately with a drizzle of high quality extra virgin olive oil, sliced chives.