Start by preparing your vegetables. Peel and chop potatoes into ¾-inch chunks.
Peel and dice onion.
Peel and chop garlic.
Cut off the dark green leaves of each leek and rinse out any dirt in its layers. Then slice thinly.
Heat olive oil in a large saucepan over medium heat.
Add chopped onions, garlic, leeks, and miso paste. Cook for 2-3 minutes, stirring frequently, until vegetables are softened but not browned and miso is fully incorporated into the vegetables.
Add potatoes and cook for another 2 minutes, stirring frequently.
Add 4 cups of vegetable stock, and bring to a simmer over medium heat. Cook for 15-20 minutes, with the pot partly covered, until potatoes are tender.
Now blend with an immersion blender until smooth.
Bring soup back to a simmer, and add coconut milk.
If soup is too thick for your liking, add as much of the extra cup of vegetable broth as desired. Heat gently for 5 minutes, to allow the flavors to meld.
Season to taste with salt and pepper.
Garnish with a swizzle of olive oil and a sprinkle of chopped chives to serve.
Notes
If you do not have an immersion blender, you can blend soup in a regular blender. Just let it cool somewhat before you ladle it into the blender—blending very hot liquid can be dangerous!It can be tricky to remove all the dirt from leeks. When you remove the outside leek layers, check to see if there is dirt between the remaining layers. If so, slice thinly and place leek slices in a bowl of cold water for 5 minutes. Remove leeks with a slotted spoon, trying not to disturb the dirt at the bottom of the bowl. Pat dry before using.