Prepare a grill for indirect heat. If using a charcoal grill, build the hot coals on one side only. If using a gas grill, heat one side only to medium-high heat.
Add the carrots, celery, corn cobs, onions, thyme, bay leaf and turkey neck to a medium pot. Add enough water to cover, place over direct heat, bring to a boil and simmer for 3 hours. Strain the stock through a fine mesh strainer.
Melt the butter or turkey drippings to a medium saucepot over medium-high heat. Whisk in the flour and cook, whisking for a few minutes, until lightly browned. Whisk in the turkey stock. Bring to a boil and simmer, whisking occasionally, about 30 minutes. Season with salt and pepper and serve.