1. Preheat oven to 425 degrees. Make filling: In a bowl, toss vegetables with oil and thyme; season generously with salt and pepper. Divide between two rimmed baking sheets. Roast 25 minutes; toss (if vegetables are sticking, sprinkle up to 1/4 cup water on each sheet). Roast until browned and tender, 20 to 25 minutes more. Transfer to a shallow 3-quart baking dish. Raise oven heat to 450 degrees.

2. Meanwhile, make topping: In a large bowl, whisk together 2 cups flour, baking powder, baking soda, salt, and pepper. Cut in butter with a pastry blender until mixture resembles coarse crumbs, with some pea-size lumps. Mix in buttermilk and cheese until combined. With a floured hand, knead dough against side of bowl until it holds together. If it is sticky, knead in up to 1/4 cup more flour.

3. In a small saucepan, bring broth and wine to a boil. Whisk in cornstarch mixture; boil 1 minute. Pour over vegetables; toss to coat. Drop small mounds of topping on vegetables; bake until brown, 15 to 20 minutes. Let cool 10 minutes; serve.