01 - Preheat the 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, cooking until the sauce thickens and smooths, about 3 to 5 minutes.
05 - Stir in ground nutmeg, salt, and black pepper. Remove the sauce from heat.
06 - Arrange half of the sliced vegetables in the baking dish in a slightly overlapping pattern. Sprinkle with half of the grated Gruyere cheese.
07 - Layer the remaining vegetables over the first and top with the remaining Gruyere cheese.
08 - Evenly pour the warm sauce over the layered vegetables and cheese.
09 - Combine breadcrumbs, Parmesan cheese, olive oil, and thyme in a small bowl. Sprinkle evenly over the top of the casserole.
10 - Cover loosely with aluminum foil and bake for 30 minutes.
11 - Remove the foil and continue baking for 20 minutes or until golden and bubbly.
12 - Allow to rest for 10 minutes before serving to set.