spinach and squash gratin

3 lb fresh spinach, stems discarded
5 tablespoons unsalted butter plus additional for greasing pan
1 small chopped onion
3 garlic cloves, minced
1 1/2 teaspoons salt
3/4 teaspoon black pepper
Rounded 1/4 teaspoon freshly grated nutmeg
1 cup heavy cream
2 large butternut squash, peeled, quartered, and seeded
1/2 oz finely grated Parmigiano-Reggiano (1/4 cup)

Bring 1 inch water to a boil in a 6- to 8-quart pot over high heat. Add spinach, a few handfuls at a time, and cook, turning with tongs, until wilted, 3 to 5 minutes. Drain in a colander and rinse under cold water. Thoroughly squeeze then coarsely chop and transfer to a bowl. Melt 3 tablespoons butter over moderately low heat, then cook onion and garlic, stirring, until softened, 3 to 5 minutes. Add onion mixture to spinach along with salt, pepper, nutmeg, and cream and stir to combine. Put oven rack in upper third of oven and preheat oven to 400°F. Butter a 3-quart shallow baking dish (13 by 9 inches; not glass). Cut squash to separate bulb section from solid neck section, then cut pieces lengthwise into 1/8-inch-thick slices with slicer. Layer squash and spinach mixture in baking dish, using about one fifth of squash and one fourth of spinach for each layer, beginning and ending with squash. Sprinkle top layer of squash evenly with cheese and dot with remaining 2 tablespoons butter, then cover directly with a sheet of parchment or wax paper. Bake until squash is tender and filling is bubbling, 25 to 30 minutes. Remove paper and bake gratin until browned in spots, 10 to 15 minutes, or broil 3 inches from heat, 2 to 3 minutes.

note: Gratin can be assembled, but not baked, 1 day ahead and kept, surface covered with parchment or wax paper and then covered with plastic wrap, chilled. Let stand at room temperature 1 hour before baking.