Set the roasting pan with the turkey drippings over medium heat on the stove. Add the vermouth and cognac, stirring with a wooden spoon to help loosen any browned bits and thoroughly deglaze. (If necessary, you can also add some of the turkey broth or stock.)
Strain the contents of the roasting pan into a large heavy saucepan, discarding the vegetable solids. Then transfer the liquid to a gravy separator. After the grease has risen to the top, pour the liquid back into the saucepan.
Add the turkey broth or stock and the chopped thyme to the degreased liquid in the saucepan. Bring the mixture to a a boil over medium-high heat. Then reduce the heat and let simmer for about 10 minutes.
Meanwhile, put the heavy cream in a liquid measuring cup (or small bowl), and whisk in the flour until the mixture is smooth. (It will be quite thick!)
Gradually whisk the cream mixture into the turkey broth or stock mixture. (And don't panic if you see some little lumps at first. These will gradually disappear as the gravy simmers.)
Bring the gravy briefly back to a boil over medium-high heat. Then reduce the heat to low, and gently simmer until the gravy has thickened, about 10 minutes. Season to taste with salt and pepper.