Arrange chicken pieces in a shallow dish.

Sprinkle with salt.

Cover and refrigerate overnight.

Drain accumulated juices and pat chicken dry.

Sprinkle with pepper.

Dredge chicken in flour.

Shake off excess flour.

Heat vegetable oil in a large iron skillet to about 1 inch deep over moderate heat.

Add chicken pieces, skin side down.

Fry slowly for 30 minutes, keeping heat moderate to low to prevent overbrowning.

Turn chicken and fry for another 30 minutes.

Add 1 tablespoon of water to the skillet (be careful of splattering).

Cover the skillet and let stand until spitting stops.

Remove chicken to paper towels to drain.

Pour oil and drippings from skillet, reserving 4 tablespoons.

Return 4 tablespoons of drippings to the skillet.

Blend in flour and cook over moderately low heat, stirring constantly, for about 5 minutes or until a nice rich brown color.

Whisk in water (or milk), salt, and pepper.

Cook, whisking constantly, for about 5 minutes or until thickened, smooth, and no raw starch taste remains.

Taste and adjust salt and pepper as needed.

Pour gravy into a heated gravy boat.

Pile the chicken onto a heated platter and serve.

Pass the gravy along with the chicken.