Preheat the oven to 425 degrees.
In a medium saucepan, bring the broth to a boil. Add the chopped potatoes, carrots and onions. Season with salt and pepper. Simmer for about 15 minutes, or until the vegetables are soft.
Meanwhile, in a small bowl, whisk together the milk and flour. When the veggies are soft, slowly add the flour-milk mixture to the pan, stirring until everything thickens. Remove pan from the heat and stir in the chicken and peas.
Add the pie filling to your 9-inch pie plate and cover with your puff pastry. This will create an awesome, flaky crust on top. Cut a few slits on top to allow steam to escape while baking. Using a pastry brush, paint with the egg wash, which will result in a nice golden sheen. This is something you can get the kids to help you with (easy enough).
Bake the pie for 25 to 30 minutes, or until the filling looks bubbly inside.