Raise the rack in your oven. You may need to run the broiler briefly to brown the potatoes.
Pre-heat your oven to 350.
Boil potatoes in well salted water.
Warm the stew in a saucepan. Add a bit of chicken stock if it seems low on liquid. You want a bit of sauce along with the meat.
Using a fork, mash the butter and flour together. You want this well mixed.
Off heat, add the butter/flour mixture to the stew and stir to combine.
Mash potatoes with 1 Tbsp of butter and the warmed milk.
Add the egg and cheese and mix.
Put the thickened stew in an ovenproof dish and top with mashed potato mixture.
Smooth the potatoes then drag a fork through the potatoes to create some texture. Or you could just use a spatula to rough up the top like I did.
Bake for about 20 minutes. Place a cookie sheet below to catch any drips.
If you want to brown the top, broil briefly but watch carefully to make sure you don't over brown the potatoes.
Let stand about 15 minutes and serve.