Preheat the oven to 400°F.
On a baking sheet, toss the delicata squash with the brown sugar, Aleppo pepper, sherry vinegar, 1 tablespoon oil and salt. Roast for 12 minutes.
Toss the yams and sweet potatoes with the remaining oil, salt and pepper on a second baking sheet. Roast for 10 minutes, until tender. Combine with the roasted delicata.
Place the fresno chiles in a heatproof bowl. Heat the remaining pickle ingredients in a saucepan. Bring to a boil, then pour the hot liquid over the chiles. Cool.
Whisk together all the pomegranate vinaigrette ingredients in a small bowl. Adjust the seasoning to taste
To serve, place the roasted squash on a plate, top with hazelnuts and pickled fresno chiles, and drizzle with pomegranate vinaigrette.