Preheat oven to 450°. Cut butternut and spaghetti squash in half lengthwise; remove and discard seeds. Place squash, cut sides up, in a lightly greased 17- x 12-inch jelly-roll pan. Drizzle with butter, and sprinkle with 1/2 cup brown sugar. Bake 40 minutes or until tender. Cool 20 minutes.
Using a fork, scrape inside of spaghetti squash to remove spaghetti-like strands, and place in a large bowl. Scoop pulp from butternut squash; coarsely chop pulp, and toss with spaghetti squash.
Stir together cinnamon, nutmeg, and remaining 1/2 cup brown sugar.
Cook cream in a heavy nonaluminum saucepan over medium heat, stirring often, 5 minutes or just until it begins to steam (do not boil); remove from heat.
Using a mandoline or sharp knife, cut potatoes into 1/8-inch-thick slices.
Arrange one-fourth of potato slices in a thin layer on bottom of a buttered 13- x 9-inch baking dish. Spoon one-third of squash mixture over potatoes (squash layer should be about 1/4-inch thick); sprinkle with 1/4 tsp. salt, 1/4 tsp. pepper, 1 cup fontina cheese, and 3/4 cup hot cream. Repeat layers twice, sprinkling one-third of sugar mixture over each of second and third squash layers. (Do not sprinkle sugar mixture over first squash layer.) Top with remaining potato slices, 1/4 tsp. salt, and 1/4 tsp. pepper. Gently press layers down with back of a spoon. Sprinkle top with remaining 1 cup cheese and 3/4 cup hot cream; sprinkle with remaining brown sugar mixture. Place baking dish on an aluminum foil-lined baking sheet.
Bake, covered with foil, at 450° for 1 hour; uncover and bake 25 more minutes or until golden brown and potatoes are tender. Cool on a wire rack 20 minutes before serving.
*Gouda cheese may be substituted.
Brought to the table by chef John Zucker of Cru Café in Charleston, South Carolina.