Pour pan juices through a sieve into a measuring cup; then let sit 10 minutes to let fat rise to the surface. Skim fat and set aside ½ cup; discard the rest. If you don't have ½ cup fat, add enough butter to make up the difference (otherwise, skip the butter).
Set roasting pan over two burners on your stovetop and turn heat to medium-high. Pour in 2 cups broth (or stock), and use a wooden spoon to scrape up any browned bits from the bottom of the pan. Pour liquid through the sieve into the measuring cup with the pan juices. Add enough extra broth (or stock) to make 5 cups liquid.
In a medium-size saucepan, heat reserved fat and any added butter over medium-high heat until sizzling. Add flour, reduce heat to medium-low, and whisk together until glossy, about 3 minutes. Slowly pour broth mixture in, whisking as you go, and cook, stirring often, until mixture thickens and flavors combine, 12-15 minutes. Add more salt and pepper to taste. Stir in Madeira and serve.