Both the filling and the potatoes can be made ahead and assembled before dinner. Slideshow: More Casserole Recipes
How to Make It
In a large pot cover the potatoes with salted water, then bring to a boil. Cook the potatoes until tender, 20 to 25 minutes. Drain the potatoes then mash together with the milk and butter. Season with salt and pepper to taste and reserve.
In a large heavy pot, heat the butter over medium high heat until hot. Brown the chicken, in batches if necessary, turning occasionally with tongs, about 6 minutes per batch. Transfer the chicken to a plate. Add the onion, celery and carrot and cook, stirring occasionally, until golden brown, about 8 minutes. Stir in the flour and cook, 3 minutes. Add the chicken with any accumulated juices back to the pot. Stir in the stock and bring to a simmer. Simmer the chicken until it is cooked and the sauce is thickened, about 10 minutes. Transfer the filling to a 3-quart baking dish. Top the chicken with the potatoes.
Bake the casserole until the filling is bubbling and the potatoes are browned in places, about 20 minutes. Serve.