Mix flour and Sherry in a small bowl until smooth paste forms. Melt butter in a heavy large saucepan over medium-high heat. Add mushrooms and rosemary: sauté until mushrooms begin to soften, about 3 minutes. (Can be prepared 3 hours ahead.) Cover flour paste lightly. Let paste and mushrooms stand at room temp.
Transfer pan juices to 8-cup glass measuring cup. Spoon off fat and discard. Add enough chicken broth to pan juices to measure 5 cups; add to saucepan with mushrooms. Add flour paste and whisk to combine. Bring mixture to boil, stirring frequently. Boil until thickened to light gravy, about 10 minutes. Mix in cream, thyme, and tarragon. Season to taste with salt and pepper. Serve with turkey.