1 teaspoon pimentón de la Vera (sweet smoked Spanish paprika)
Freshly ground pepper
In a large pot, heat the oil. Add the turkey wings, turkey neck (if using) and chicken wings and cook over moderately high heat until browned all over, 7 to 8 minutes; transfer to a baking sheet. Add the smoked turkey leg and wings to the pot and cook, turning, until lightly browned, 3 to 4 minutes; transfer to the baking sheet.
Add the onion, carrots, garlic, peppercorns and chile (if using) to the pot and cook over moderate heat, stirring, until the vegetables are golden, 5 minutes. Return all of the turkey and chicken to the pot along with any accumulated juices. Stir in the broth and 4 cups of water. Bring to a boil, cover partially and simmer until the stock is smoky and reduced to 5 cups, 1 hour. Strain the stock into a large bowl or measuring cup and discard the solids.
In a large saucepan, melt the butter. Whisk in the flour and cook over moderate heat, whisking, until the roux is tan, 3 minutes. Add the pimentón and cook, whisking, for 1 minute. Whisk in the strained stock and cook over moderate heat, whisking, until thickened, 5 minutes. Season the gravy with salt and pepper and serve warm.