01 - Preheat oven to 375°F. Generously grease a 9x13-inch baking dish with butter.
02 - In a saucepan over medium heat, melt 2 tablespoons butter. Add minced garlic and onions; sauté until softened, about 3 minutes.
03 - Add cream, milk, thyme, nutmeg, salt, and pepper to the saucepan. Heat the mixture until just steaming, then remove from heat.
04 - Arrange half the potatoes, parsnips, carrots, and squash in the prepared dish. Season lightly with salt and pepper.
05 - Sprinkle half of the grated Gruyere cheese evenly over the vegetables.
06 - Repeat the layering process with the remaining vegetables and cheese.
07 - Pour the warm cream mixture evenly over the layered vegetables and cheese.
08 - Sprinkle breadcrumbs over the top of the gratin if desired.
09 - Cover the dish with foil and bake for 40 minutes. Remove foil and bake for an additional 20 minutes, or until the top is golden and vegetables are tender.
10 - Let the gratin rest for 10 minutes before garnishing with extra thyme and serving.