Drop the chicken breast with bone and skin into a medium saucepan that has at least 1 quart of boiling water. When it comes to a boil again, turn the heat down to low and let the chicken simmer for 25 minutes.
Remove and cool the chicken, then cut it into 1-inch cubes. Set the chicken aside. Place the skin and bones back into the simmering water and let this continue to simmer for as long as you want. This becomes your chicken broth.
Add the carrots, celery, and potatoes to the broth. Continue simmering for 15 minutes. Simmering the vegetables in the chicken broth is necessary and preserves their vitamins. The chicken skin and bones are very good for you. The skin is loaded with collagen.
Discard the skin and bones after their nutrients have been cooked into the broth. Set the vegetables aside.
Melt the butter in another saucepan over medium heat. Add the onion and cook until soft and translucent (about 5-6 minutes). Stir in the flour and seasonings. Then slowly stir in the chicken broth and milk. Continue cooking and stirring until smooth and thick. Set aside.
Cut the butter into pieces.
Whisk the flour and salt together and put into the food processor. Add the butter pieces and pulse the mixture until the flour looks like corn meal evenly dispersed. The butter needs to coat each grain of flour. Transfer the mixture to a bowl.
In the 2-cup measuring cup put ½ cups apple cider vinegar, ½ cups water and 5 ice cubes. Stir the apple cider vinegar and water until the mixture is cold. Remove the unmelted ice.
Slowly spoon the ice water vinegar mixture into the bowl 1 tablespoon at a time while gently rocking the bowl, letting the wet mixture soak into the dough. A one-crust pie requires 5-7 tablespoons of the cold vinegar water, so for this two-crust pie you should stop after 10 tablespoons and check the mixture carefully. You want to add only enough of the apple cider vinegar and water until the dough begins to hold together so that you can form two same sized balls to roll out for the bottom and top pastry crusts. Handle the pie dough as little as possible to keep it flaky.
With minimal handling, carefully separate the dough into two same-sized balls. Refrigerate one of the balls to be used for the top crust until you can roll it out.
Sprinkle a generous amount of flour evenly over the pastry cloth and press and roll out the bottom crust to about a 12-inch circle. Then try to roll this up around the rolling pin so that you can transfer and unroll this bottom crust into the pie plate. Good luck! Not to worry if it breaks a little.
Add the vegetables along with the frozen peas evenly over the bottom crust. (The peas don’t have to be pre-cooked. The half hour of baking will make them just right.) Then add the chicken also dispersing it evenly.
Pour the chicken broth and milk over all.
Roll out the top crust and place it on the pie. Cut slits in the top crust to allow air to escape. Using a fork or knife handle pressed between your thumb and forefinger, go around the edge of the finished pie making indentions for decoration.
Bake at 425° for 30 to 35 minutes.
Serve and enjoy!