Set the roasting pan with the turkey drippings and vegetables over two burners set on medium high. Add the Cognac, vermouth, and 1/2 cup of the turkey broth; cook, stirring with a wooden spoon or wooden spatula to loosen the browned bits in the pan, until the liquid comes to a simmer. Strain the contents of the roasting pan through a large sieve and into a large saucepan. Add the remaining 2 cups turkey broth and the thyme to the saucepan and bring to a boil over medium-high heat; reduce the heat and let simmer to blend the flavors, about 5 minutes.

Meanwhile, put the cream in a small bowl and whisk the flour into the cream to make a smooth paste. Gradually whisk the cream mixture into the turkey broth mixture. Bring to a boil over medium-high heat, reduce the heat to low, and gently simmer to thicken the gravy and cook off the raw flour flavor, about 10 minutes. Keep hot until ready to serve.