Both the filling and the potatoes can be made ahead and assembled before dinner. Slideshow: More Casserole Recipes
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.
Not terrible, just a bit dull.