Pour drippings through a fine wire-mesh strainer into a large measuring cup; skim off fat into a separate measuring cup. (Add melted butter to fat to equal 1/2 cup, if necessary.)
Pour broth into a large bowl. Stir in 1 cup strained pan drippings.
Heat 1/2 cup reserved fat in a medium saucepan over medium heat. Whisk in flour and next 2 ingredients. Cook, whisking constantly, 5 minutes or until golden brown. Whisk in sherry; cook, whisking constantly, 2 minutes. Whisk in chicken broth mixture in a slow, steady stream. Bring to a boil; reduce heat, and simmer 5 minutes. Season with kosher salt and black pepper to taste.