Make filling: Bring the broth to a boil in a saucepan. Add the carrot and celery and cook until tender, about 4 minutes. Using a slotted spoon, transfer them to a plate.
Pour enough of the broth into a liquid measure to make 2 1/2 cups. Set aside.
Heat the butter in a large saucepan over medium-high heat. Add the mushrooms and cook, stirring, until lightly browned, about 6 minutes. Add the shallot, bay leaf, thyme, and tarragon and cook, stirring, until soft. Stir in the flour and cook, stirring, for 3 minutes. Gradually stir the reserved broth, wine, nutmeg, and season with salt and pepper. Bring the sauce to a boil, lower the heat, and simmer, stirring occasionally, about 4 minutes.
Add the carrot, celery, chicken, onions, and peas and return to a boil. Stir in sherry and remove the chicken mixture from the heat. (Filling may be made 1 day ahead, cooled, uncovered, and chilled, covered.)
Preheat oven to 425 degrees F.
Make mashed potatoes: In a saucepan cover potatoes with water by 1 inch and simmer until very tender, 10 to 15 minutes.
Reserve about 1/3 cup cooking liquid and drain potatoes. In batches, force potatoes through a ricer into a bowl. Stir in sour cream, chives, and enough reserved cooking liquid to reach a fluffy consistency. Season with salt and pepper, to taste.
Transfer potatoes to a pastry bag fitted with a 1/2-inch fluted tip. Spread filling in a 1 1/2 to 2-quart gratin dish or other shallow baking dish. Pipe mashed potatoes decoratively in mounds on filling and bake in middle of oven until filling is bubbling and potatoes are golden on edges, about 25 minutes.
Each serving: About 411 calories, 10.7 grams fat (23 percent of calories from fat).