Preheat oven to 400º. In a small bowl, combine shallot, vinegar, and ½ teaspoon salt. Let sit, stirring occasionally, while vegetables roast.
On a large rimmed baking sheet, toss fennel, squash, apple, oil, 1 teaspoon salt, and ½ teaspoon pepper with your hands. Transfer some of the fennel mixture to another baking sheet so vegetables are in an even layer.
Roast vegetables, rotating pans halfway through, until golden brown and tender, 35 to 45 minutes.
Transfer vegetables to a platter. Top with pickled shallots, hazelnuts, pomegranate seeds, and parsley.
