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 an 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 a light gravy, about 10 minutes. Mix in cream, thyme, and tarragon. Season to taste with salt and pepper. Serve with turkey.