Preheat oven to 400°F.

Peel, seed, and cube the butternut squash into 3/4- to 1-inch pieces.

In a large bowl, toss butternut squash cubes with olive oil, coarse kosher salt, and ground pepper.

Spread squash cubes on a large rimmed baking sheet.

Roast until just tender and beginning to brown, stirring occasionally, for about 35 minutes.

Meanwhile, melt 3 tablespoons of butter in a heavy medium skillet over medium-low heat.

Add sliced leeks and chopped fresh sage to the skillet.

Sprinkle with salt and pepper.

Sauté until tender but not brown, about 15 minutes.

Coat an 11x7-inch baking dish with the remaining 1 tablespoon of butter.

Spread half of the leek mixture over the bottom of the prepared baking dish.

Sprinkle with half of the roasted squash and half of the goat cheese.

Repeat layering with the remaining leeks, squash, and goat cheese.

Preheat oven to 375°F.

Pour heavy cream evenly over the gratin.

Sprinkle with toasted chopped hazelnuts.

Bake uncovered until gratin is heated through and cream is bubbling, about 30 minutes (40 minutes if previously chilled).