Preheat oven to 400 degrees.
In a medium saucepan cover the diced potatoes and frozen vegetables with water and boil for about 7-8 minutes, until potatoes are softened. Strain and set aside.
In a separate saucepan. melt the butter over medium heat and then add the flour, stirring until well combined. Add the salt and pepper and stir.
Add the chicken broth and milk and whisk until smooth. Continue to heat the mixture, stirring occasionally until it begins to bubble. Let boil for about a minute and then remove from heat.
Add chicken and vegetables to the mixture and stir until well combined.
Scoop mixture into four 8-ounce oven-proof dishes or one pie plate.
If you are making four individual pot pies, roll out the pie crust cut into fourths. Place each fourth over each pot pie and press the edges down over the rim. Use a knife to cut two or three slits in the top so that the steam can escape. If you are making one large pot pie, you'll do the same thing but just leave the entire crust intact and place over the filling in the pie plate.
Bake for 40 minutes (for the small pot pies) or 45-50 minutes for the larger one. The crusts should be golden brown and the filling should be bubbly when done.