01 - Preheat oven to 375°F (190°C). Butter a 9x13-inch (23x33 cm) baking dish.
02 - Peel and thinly slice butternut squash, parsnips, Yukon Gold potatoes, and leeks.
03 - Melt butter over medium heat in a saucepan. Stir in flour and cook for 1 minute, stirring constantly.
04 - Gradually whisk in milk and cream. Cook, whisking frequently, until thickened and smooth, about 3 to 5 minutes.
05 - Remove from heat and stir in nutmeg, salt, and black pepper.
06 - Arrange half of the sliced vegetables in the prepared dish, slightly overlapping. Sprinkle with half the Gruyere cheese. Repeat with remaining vegetables and cheese.
07 - Evenly pour the warm sauce over the layered vegetables and cheese.
08 - In a small bowl, combine breadcrumbs, Parmesan, olive oil, and thyme leaves. Sprinkle mixture evenly over the gratin.
09 - Cover the dish loosely with aluminum foil and bake for 30 minutes.
10 - Remove foil and bake an additional 20 minutes until the topping is golden and the gratin is bubbly.
11 - Allow to rest for 10 minutes before serving.