Melt butter in a heavy-bottomed pot (like a dutch oven) over medium-low heat. Add leeks and a pinch of kosher salt. Reduce temp to low, and cook low and slow for 10-15 minutes until very soft with little to no browning.

Stir in garlic, potatoes, thyme, bay leaves, vegetable broth, ½ tsp kosher salt, and a couple turns of black pepper. Bring to a low boil, cover, and reduce heat to simmer for 10 minutes until potatoes are soft and fall apart easily.

Fish out potatoes and press through a potato ricer into a separate bowl. Add leeks and broth to a blender (remove bay leaves and thyme stems). Blend on low then slowly increase to high until smooth. Add back to pot and whisk in riced potatoes, non-dairy milk, and coconut milk.

Bring soup to a simmer then whisk in grated nutmeg. Season with kosher salt (~½ tsp) and pepper (couple turns) to taste. Serve with chopped fresh chives and toasted bread.