Bring a large pot of lightly salted water to a boil.
Add the chicken to the water and simmer 8 to 10 minutes for a chicken breast that was thawed and 10 to 12 for a breast that was frozen, then add:
carrots, celery, potatoes, and onion to the boiling water with the chicken and cook until just barely tender; an additional 10 minutes or so.
Remove the chicken and and vegetables to a bowl and set aside.
Collect one cup of cooking liquid from the pot and pour out the rest.
Add the bullion cube or chicken base (if using it)to the reserved water from the pot and stir until it's mostly dissolved. Add one cup of milk to the water and set aside.
Preheat your oven to 400.
Clean the cooked chicken removing any tough parts, bone or skin (if you had it) and dice the chicken into 1/2 inch chunks. Place the chicken and vegetables into a deep dish pie plate or pie plate that can hold the filling with about 1/2" of space at the top. Set aside
In the same pot you used before, melt the butter and add the flour. Stir one minute over medium heat until the mixture is bubbly and golden.
Add the milk and water mixture and turn the heat up to medium high. Add salt and pepper.
Stir frequently until the mixture starts to bubble and coats the back of a spoon--about 6-8 minutes.
Pour the sauce over the chicken and vegetables.
Cover with the crust and crimp the edges.
Cut a couple of small holes in the top to vent the pie as it cooks.
Bake on a cookie sheet to catch any sauce that boils over.
Bake at 400 for 20 to 25 minutes or until the crust is golden