Strain the pan drippings into a fat separator or large measuring cup. Let stand for 10 minutes.
Skim and discard the fat from the surface.
Place the empty roasting pan over 2 burners over medium-high heat. Add the wine and cook for 2 minutes, stirring and scraping to dissolve any bits stuck to the pan. Remove from heat and pour into the cup with the pan juices.
Melt the butter in a large skillet over medium heat. Sprinkle with the flour and cook, stirring constantly, until golden brown, about 5 minutes. Still stirring, slowly add the broth, then the reserved pan juices and sprigs of thyme. Bring to a boil, reduce heat, and simmer until thickened, about 10 minutes. Remove from heat and stir in 1 teaspoon salt and 1/2 teaspoon pepper. Remove and discard the thyme before serving.