Instructions: With a vegetable peeler, pare skin from squash and discard. Cut squash in half lengthwise, and scoop out and discard seeds. Cut squash into 1/4-inch-thick slices, then cut enough into neat 1/4-inch cubes to make 2 cups; chop remainder.

In a 3- to 4-quart pan over high heat, bring broth to a boil. Add squash cubes and cook until barely tender when pierced, 3 to 4 minutes. With a slotted spoon, transfer cubes to a bowl.

To pan, add chopped squash, garlic, vinegar, and rosemary. Boil, stirring occasionally, until most of the liquid is evaporated and squash mashes easily when pressed, about 30 minutes.

Meanwhile, rinse, drain, and quarter shiitake mushroom caps. In a 10- to 12-inch frying pan over high heat, combine 2 tablespoons butter and shiitakes; stir often until mushrooms are lightly browned, 5 to 6 minutes.

In a blender or food processor, combine chopped squash mixture, chestnuts, and 2 tablespoons butter; whirl until smooth. Scrape into a shallow 1 1/2-quart casserole (microwave-safe if making ahead). Scatter cooked cubed squash and mushrooms over pureed squash mixture. Add salt and pepper to taste.

Roasted Chestnuts: Sort chestnuts, discarding those that feel very light (they are apt to be moldy), to make 1 pound (about 4 cups) nuts. Cut an X through the flat side of each shell. Spread chestnuts in a single layer in a 10- by 15-inch baking pan. Bake in a 400 degree oven until nuts are no longer starchy-tasting (taste to test), about 30 minutes. Wrap hot nuts in a towel and enclose in a plastic bag; let stand until cool enough to touch, about 10 minutes. Take out 1 nut at a time and, with a short-bladed knife, pull off and discard shell and as much of the brown skin as you can. Use warm or cold. (Makes 2 cups)

This recipe yields 6 to 8 servings.

Comments: Instead of roasting fresh chestnuts, you can use peeled cooked chestnuts, which are available frozen, vacuum-packed and shelf-stable, and packed in water and canned. If making casserole up to 1 day ahead, cool, cover airtight, and chill; to reheat, uncover and cook in a microwave oven on full power (100%) until hot, about 4 minutes.

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