Preheat the oven to 375°F (190°C).
Grease a 9x13-inch baking dish with butter.
Layer the sliced potatoes, carrots, and parsnips in the baking dish.
In a saucepan, sauté the onions until translucent.
Pour the heavy cream over the layered vegetables.
Sprinkle cheese, thyme, salt, and pepper over the top.
Top with breadcrumbs to create a crust.
Cover with foil and bake for 30 minutes.
Remove the foil and bake for an additional 15-20 minutes until golden.
Let cool slightly before serving.