Heat the oven to 375°F. Put the chicken wings in a large roasting pan, drizzle with the oil, and sprinkle liberally with salt and pepper. Toss to coat and spread the wings out in a single layer.
Roast, undisturbed, until the bottom of the pan is coated with fat and the wings are beginning to brown, about 15 minutes. Use a spoon to baste the wings with the drippings, then carefully pour the extra fat out of the pan and flip them over (if they're sticking give them an extra 5 minutes).
Return wings to the oven until both sides are nicely browned, another 10 minutes or so (they'll release easily from the pan when ready).
Raise the oven temperature to 450°F and continue to cook until wings are crisp all over, about 10 minutes. Serve hot, warm, or at room temperature with carrot and celery sticks on the side.