Heat the olive oil in a large saucepan over medium heat until hot. Add the onion, celery, carrot, and cinnamon stick and saute until soft but not brown, about 10 minutes. Season with salt and pepper.

Add the chicken stock and the coriander, if using, and bring to a boil. Simmer for several minutes. Stir in the squash until smooth, then simmer gently to let the flavors meld, about 10 minutes. Discard the cinnamon stick.

Puree the soup in a blender until smooth. (The soup can be made ahead to this point, cooled, covered, and refrigerated for several days or frozen for about 1 month. It will thicken as it cools and may need thinning with stock or water when reheating.)

Return the soup to the pan and reheat gently. Add the half-and-half, if using. Adjust the seasoning with salt and pepper. Keep warm until service.

Ladle the soup into serving bowls. Garnish evenly, with the cheese and pumpkin seeds, if desired.

Preheat the oven to 400 degrees F. Peel the squash with a vegetable peeler. Halve lengthwise, discard the seeds, then cut into 1-inch dice. Place in a large bowl and season with salt and pepper.

Heat the butter in a medium skillet over medium-high heat. When the butter ceases to foam and has turned a light brown, pull the pan off the heat and immediately add the sage, sugar, vinegar (stand back so as not to get splattered), molasses and toasted spice rub. Mix well and let simmer over medium-low heat for 1 to 2 minutes to meld the flavors.

Pour the vinegar mixture over the squash and toss well, then transfer to a heavy rimmed baking sheet or baking dish large enough to hold the squash in a single layer. Place in the oven and roast, tossing at least once, until very tender and caramelized, about 45 minutes to 1 hour. Set aside until cool enough to handle but still warm, so the liquids are runny.

Working in batches, if necessary, transfer the warm squash and all the cooking liquids to a food processor and process until smooth. Use immediately, refrigerate for up to 5 days, or freeze for up to 2 months.

Serving suggestions: Serve the puree on its own as a side dish for roast chicken, turkey, or pork; stir into polenta just before the end of cooking; use as a stuffing for ravioli; make into a soup; or use to flavor pastina. Or omit the sage, season with ground cinnamon and freshly grated nutmeg to taste, and use as a substitute for canned pumpkin in your favorite pumpkin pie recipe.

Variation for Smoky Butternut Squash: Cook the prepared squash on a baking sheet in a covered grill with soaked chips to give a slightly smoky taste. Substitute in any of the recipes that call for roasted squash. If cooking kabocha, acorn, or other difficult-to-peel squash, cut in half, scoop out the seeds, and rub the insides and cut edges with the vinegar/molasses mixture. Place on a baking sheet, cut sides up, and roast at 400 degrees F until tender. Scoop out and puree.

Yield: about 2 cups puree

Toast the fennel seeds, coriander seeds, and peppercorns in a small, heavy pan over medium heat. When the fennel turns light brown, work quickly. Turn on the exhaust fan, add the red pepper flakes, and toss, toss, toss, always under the fan. Immediately turn the spice mixture out onto a plate to cool.

Put mixture into a blender with the chili powder, salt, and cinnamon and blend until the spices are evenly ground. If you have a small spice mill or a coffee grinder dedicated to grinding spices, grind only the fennel, coriander, pepper, and chili flakes. Pour into a bowl and toss with the remaining ingredients. Keep the spice mix in a glass jar in a cool, dry place, or freeze.

Chef's notes: Toasting freshens spices, releases their oils, and makes them more fragrant, as well as adding a new dimension of flavor.

Taste your chili powder before adding and, if spicy and hot, cut back the amount. California chilies are almost sweet, not hot.

Yield: about 1 cup