Strain the drippings into a large measuring cup or bowl. Let stand for 5 minutes, then skim off and discard the fat. (Alternatively, use a fat separator.)
Place the empty pan over 2 burners over medium-high heat. Add the cider and cook for 1 minute, scraping up the bits stuck to the pan. Pour into the skimmed drippings and add enough broth to make a total of 4 cups.
Melt the butter in a large saucepan over medium heat. Cook the flour, whisking, until golden, 4 to 5 minutes. Whisk in the broth mixture and bring to a boil. Reduce heat and simmer until thickened, 8 to 10 minutes. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Strain.