Serve this savory upside-down tart with a leafy green salad for a great vegetarian dinner.
Preheat oven to 400 degrees. In a 10-inch ovenproof skillet, heat oil over medium-high. Add onion, thyme, and sugar and cook until onion is softened, about 8 minutes; season with salt and pepper. Reduce heat to medium and spread onions evenly in pan. Add parsnips in an even layer, cover, and cook until almost tender, 8 minutes.
On a lightly floured work surface, trim pastry into a 10-inch round. Top parsnips with pastry. Bake until pastry is puffed and golden, 20 minutes. Let cool on a wire rack, 10 minutes, then invert.