01 - Preheat oven to 375°F. Butter a 9x13-inch baking dish.
02 - Peel and thinly slice butternut squash, parsnips, potatoes, and leeks.
03 - Melt butter in a saucepan over medium heat. Stir in flour and cook for 1 minute.
04 - Gradually whisk in whole milk and heavy cream. Cook, whisking, until sauce thickens and is smooth, about 3 to 5 minutes.
05 - Stir in ground nutmeg, salt, and black pepper. Remove from heat.
06 - Arrange half the sliced vegetables in the prepared dish, slightly overlapping. Sprinkle with half the grated Gruyere.
07 - Add remaining vegetables over the first layer and top with the remaining Gruyere cheese.
08 - Evenly pour the warm sauce over the layered vegetables and cheese.
09 - In a small bowl, combine fresh breadcrumbs, grated Parmesan, olive oil, and thyme leaves. Sprinkle evenly over the gratin surface.
10 - Cover loosely with aluminum foil and bake for 30 minutes. Remove foil and continue baking for another 20 minutes or until golden and bubbly.
11 - Allow the gratin to rest for 10 minutes before serving to set.