01 - Preheat the oven to 375°F. Grease a 9x13-inch baking dish with butter or oil.
02 - In a medium saucepan over medium heat, melt butter. Whisk in flour constantly for 1-2 minutes until lightly golden.
03 - Gradually whisk in milk and cream. Add Dijon mustard, nutmeg, salt, and pepper. Cook while whisking until sauce thickens, about 5 minutes. Remove from heat and stir in half the Gruyère cheese.
04 - In a large bowl, toss sliced potatoes, squash, parsnips, carrots, leek, and garlic with salt, pepper, and half the thyme.
05 - Arrange half the vegetables in the prepared baking dish and pour half the sauce over them. Repeat layers with remaining vegetables and sauce.
06 - Sprinkle the top with remaining Gruyère, Parmesan, breadcrumbs, and remaining thyme.
07 - Cover loosely with aluminum foil and bake for 35 minutes.
08 - Remove foil and bake an additional 15 minutes until the top is golden and vegetables are tender.
09 - Allow to rest for 10 minutes prior to serving.