Heat cooking oil in a 3-quart saucepan over medium-high heat. Add leeks and garlic. Cook, stirring frequently, until the vegetables are tender.
Add the squash, 4 cups of the stock, the nutmeg, cumin, salt, and pepper. Bring to boiling; reduce heat. Cover and simmer about 25 minutes or until squash is very soft.
Strain vegetables, reserving cooking liquid. Put vegetables in batches in a blender container or a food processor bowl. Cover and blend or process until smooth, adding a little cooking liquid, if needed, to make the mixture a very smooth puree.
Return puree to saucepan with reserved cooking liquid. Add the corn and the 3 tablespoons cream; stir until combined. If necessary, stir in enough of the remaining stock to make a medium-thick consistency. Adjust the seasonings and heat through. Serve hot, garnished with some additional whipping cream and chives, if you like. Makes 10 to 16 side-dish servings.
To make the soup ahead, tightly cover and refrigerate for up to 3 days or freeze it for up to 3 months.