Preheat oven to 400 degrees F. Coat a 1 1/2-quart gratin dish or other shallow baking dish with cooking spray.
Heat oil in a large nonstick skillet over medium-high heat. Add onions and cook, stirring frequently, until golden and caramelized, 8 to 10 minutes. Stir in prunes, thyme, salt and pepper; remove from the heat.
Spread half the parsnips in the prepared dish. Cover with the onions and prunes. Top with the remaining parsnips and pour in broth. Tightly cover the dish with aluminum foil and bake until the parsnips are very tender, about 1 hour.
Remove from the oven. Set the oven to broil. Uncover the dish and baste the top with juices. Broil until the top begins to brown, 3 to 4 minutes.
1 1/2 starch, 1/2 fruit, 1 vegetable