Adjust oven rack to middle position and heat oven to 450 degrees. Line baking sheet with parchment paper. Stir Bisquick, ¾ cup broth, Gruyere, 1 tablespoon tarragon, and pepper together in bowl until combined. Using two greased soupspoons, scoop out and drop 12 even mounds of dough onto prepared baking sheet (about 2 heaping tablespoons per mound). Bake until biscuits are puffed and lightly browned on bottom, about 10 minutes.

Meanwhile, heat oil in 12-inch skillet over medium-high heat. Add leeks and mushrooms and cook until softened and lightly browned, 5 to 7 minutes. Stir in lour and garlic and cook until lightly browned, about 1 minute. Gradually whisk in remaining 2¼ cups broth and cream, scraping up any browned bits and smoothing out any lumps, and simmer until thickened, 3 to 5 minutes. Stir in shredded chicken, peas, and remaining 1 tablespoon tarragon. Off heat, season with salt and pepper to taste.

Grease 13 by 9-inch baking dish and transfer chicken mixture to prepared dish. Place biscuits on top and bake until filling is bubbling and biscuits are browned, about 10 minutes. Let cool slightly and serve.