Preheat your oven to 375°F (190°C) and lightly grease a baking dish.
Combine sliced parsnips, cubed kohlrabi, and sweet potatoes in a large bowl. Drizzle with olive oil, season with salt, pepper, and chopped thyme, then toss to coat evenly.
Spread the seasoned vegetables evenly in the prepared baking dish, creating a layered base.
Bake the vegetables uncovered for about 25-30 minutes, or until they are tender and slightly browned around the edges.
While the vegetables bake, prepare the crispy topping by mixing bread crumbs with melted butter and chopped thyme in a small bowl.
Sprinkle the shredded cheese evenly over the roasted vegetables, then spread the buttered bread crumb mixture on top.
Return the dish to the oven and bake for an additional 10-15 minutes, until the topping is golden brown and crispy, and the cheese is melted and bubbly.
Remove from the oven and let it rest for a few minutes. Serve warm to enjoy the soft vegetables contrasted with the crunchy topping.