Melt butter in a large stockpot over medium heat. Saute the onion, garlic, carrots, and celery with 4 sprigs each parsley and thyme, 4 sage leaves, and 2 bay leaves until fragrant. Deglaze the pan with 1/4 cup cognac, cook for 2 minutes to evaporate the alcohol. Sprinkle in flour to tighten up the mixture and stir to dissolve. Pour in the chicken broth a little at a time to avoid lumping. Add the smoked turkey wings and water, simmer for 15 minutes while preparing the giblets.
Coat a saute pan with olive oil and place over medium-high heat. Add the turkey giblets and neck, along with the remaining herbs. Season with salt and pepper. Add 2 tablespoons cognac and continue to cook until the giblets are cooked through. Remove the giblets from the pan and chop them up.
Pass the broth through a strainer to remove the large pieces of turkey and vegetables. Return the broth to the stove and add the giblets. Simmer until the gravy is thick enough to coat the back of a spoon. Stir in peppercorns and serve with turkey.