Preheat oven to 400F.
On a high-sided baking sheet, drizzle 2 turns of the pan of EVOO and place in the oven to get really hot.
Fill a high-sided saut pan with about 2 inches of water and place over high heat. When simmering, cook parsnips until tender, about 4 minutes.
While the parsnips are cooking, mix the pecans, breadcrumbs and Parmigiano-Reggiano in a shallow dish, place the flour in a separate dish with salt and ground black pepper, and beat the egg in another shallow dish. When the parsnips come out of the water, let them cool.
Once the parsnips are cool enough, toss them in the seasoned flour, then in the egg and then into the pecan, breadcrumb and cheese mixture. Carefully put the parsnips onto the oiled baking sheet, and roast until tender and golden brown, about 10 minutes, tossing about halfway through.
Combine the barbecue and chili sauces and serve alongside the parsnips as a dip.