Preheat your oven to 375°F (190°C). Toss the chopped root vegetables with olive oil, dried thyme, salt, and pepper in a large mixing bowl until evenly coated.
Spread the seasoned vegetables in an even layer on a baking sheet. Roast for about 25-30 minutes, or until tender and lightly caramelized, stirring once halfway through to promote even cooking.
While the vegetables roast, prepare the crunchy topping by mixing breadcrumbs, grated Parmesan, and melted butter in a small bowl until crumbly and evenly coated.
Transfer the roasted vegetables to a greased baking dish, spreading them out evenly. Pour the vegetable broth over the vegetables to add moisture and help steam a bit while baking.
Sprinkle the breadcrumb mixture evenly over the top of the vegetables, pressing down gently to ensure good contact and adhesion.
Bake the assembled casserole in the preheated oven for an additional 15-20 minutes, or until the topping is golden brown and crispy, and the casserole is bubbling around the edges.
Remove the casserole from the oven and let it rest for a few minutes. The aroma of roasted vegetables and toasted breadcrumbs fills the air.
Serve the casserole warm, spooned onto plates, showcasing the tender vegetables topped with a crispy, cheesy crust.
