Heat the coconut oil in a medium saucepan over medium heat. Add the shallot and scallion whites and cook, stirring, until tender, 3 to 4 minutes. Add the potato, ginger, cayenne, bay leaf, 1/2 teaspoon salt and a few grinds of pepper and cook, stirring, until the potatoes are well coated, 2 to 3 minutes. Pour in the broth and bring to a simmer.
Add the butternut squash and simmer until the potatoes and squash are tender, about 20 minutes, adjusting the heat as needed to maintain a simmer. Remove from the heat, discard the bay leaf and let cool at least 5 minutes. Carefully puree until smooth with a handheld immersion blender or in 2 to 3 batches in a blender (do not fill blender more than halfway full).
Stir in the coconut milk and reheat the soup if necessary, adjusting the consistency with water and seasoning with additional salt and pepper.
Serve hot sprinkled with chopped cilantro and scallion greens and a drizzle of coconut milk if using.
When blending hot liquid, first let it cool for 5 minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters and pulse until smooth.
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