This spicy, slightly sweet, and richly textured soup is a wonderful addition to a Thanksgiving meal, but its warming satisfaction can be enjoyed throughout the fall and winter. Kabocha squash is loaded with nutrients, so much so that in Japan there is a saying: "Eating kabocha on the first day of winter keeps you from catching a cold." Because uncooked kabocha squash can be difficult to cut, I bake the whole squash, wrapped in aluminum foil, in the oven for about 1 ½ hours until very tender.
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*Note: Be very cautious when puréeing hot liquids. If using a blender, remove the plug in the top and cover the hole with a thick kitchen towel that's folded over. Do not fill the blender or food processor more than half full.
Preheat the oven to 400 degrees.
Wrap the kabocha squash in aluminum foil. Put the squash in the oven and bake for 1 ½ hours. Remove the squash from the oven and carefully remove the foil. Cut the squash in half and remove the seeds with a spoon, removing as little pulp as possible. Scoop out the pulp into a large bowl and measure out 2 1/3 cups of cooked squash. Freeze any extra pulp for later use, and reserve ¼ cup of the green skin, julienned, for garnish.
Place the carrot, leek, and stock in a medium-sized pot, cover, and cook over medium-high heat. Bring to a boil, reduce the heat to medium-low, and simmer until the vegetables are tender, for 25 minutes.
Working in 3 or 4 batches, transfer the broth and cooked vegetables along with the pulp of the squash to a blender or food processor, and purée until smooth.* Transfer the first puréed batch to a clean pot and repeat the process. In the last batch, add the ginger juice, cinnamon, nutmeg, miso, salt, and olive oil and process.
Before serving, gently reheat the soup and divide it into soup bowls. Add a tiny pinch of salt to each bowl, garnish each bowl with the julienned green squash skin and pumpkin seeds, and serve.