01 - Preheat oven to 375°F. Lightly grease a 9x13 inch baking dish with butter or oil.
02 - Melt butter in a saucepan over medium heat. Whisk in flour continuously for 1-2 minutes until lightly golden.
03 - Gradually whisk in whole milk and heavy cream. Add Dijon mustard, nutmeg, salt, and pepper. Cook, whisking, until sauce thickens, about 5 minutes. Remove from heat and stir in half the Gruyère cheese.
04 - In a large bowl, combine sliced potatoes, butternut squash, parsnips, carrots, leek, and garlic. Season with salt, pepper, and half the thyme. Toss to coat evenly.
05 - Place half the vegetables in the baking dish in an even layer. Pour half the sauce over. Repeat with the remaining vegetables and sauce.
06 - Sprinkle the top with remaining Gruyère, Parmesan, breadcrumbs, and the rest of the thyme.
07 - Cover loosely with foil and bake for 35 minutes.
08 - Remove foil and continue baking for an additional 15 minutes, until the topping is golden and vegetables are tender.
09 - Allow to rest for 10 minutes before serving.