Preheat oven to 425 degrees. Drizzle parsnips with oil, and season with salt and pepper. Arrange on a rimmed baking sheet. Roast, shaking occasionally, until caramelized and tender, 23 to 25 minutes. Let cool. Reduce heat to 375.
Heat 2 tablespoons butter over medium heat in a medium saute pan until melted. Add leeks, and cook, stirring occasionally, until tender, about 5 minutes. Remove from heat; add wine, and return to heat. Let simmer until reduced, 1 minute. Add thyme, and remove from heat. Stir in roasted parsnips.
Whisk together melted butter, heavy cream, eggs, and 3/4 cup Parmesan in a large bowl. Season with salt and pepper. Add leek-parsnip mixture, then fold in bread. (Mixture can be refrigerated overnight.)
Butter a shallow 2-quart baking dish, and pour parsnip mixture into dish. Cover loosely with parchment, then foil, and bake until golden brown and puffed, 50 minutes. Remove parchment and foil. Sprinkle with remaining 1/4 cup Parmesan, and return to oven. Bake for 10 minutes more. Let stand for 5 minutes before serving.
To make this savory pudding ahead of time, assemble and refrigerate it for up to one day. Let stand at room temperature for 10 to 15 minutes, and bake as instructed.