In a large frying pan on medium heat, add the butter and onion. Cook for about 3 minutes, stirring often, until the onion has softened a little.
Add the diced chicken to the pan with the onion and cook it most of the way through, which will take about 5 minutes.
In a medium saucepan, make a paste with the cornstarch and some of the water, continually stirring. Add in the remainder of the water and the milk and cook this mixture for about 3 minutes, stirring all the time until it has thickened.
Add the peas, and carrots mixture, and seasonings to the saucepan. Cook on medium low heat for about 5 minutes, while occasionally stirring.
Add the chicken to the vegetable mix, gently combine them all well and let the mixture cool a little, before adding it to the pie crust base.
While the filling is cooling, roll out the top crust.
Roll out the dough on parchment paper dusted with flour. This will make it easier to transfer the rolled out dough to the top of the pie.
Transfer the cooled filling to the pie crust base.
Roll the crust up in the parchment paper and then gently unroll it, on top of the pie filling. Use a fork to seal the edges and poke a couple of holes in the top crust.
Bake the pie in the oven for 10 minutes, then reduce the heat to 400℉ and bake the pie for another 10 minutes, until the crust in golden and the filling is bubbly. Cover the top of the pie with tin foil if you think the crust is browning too much. Let the pie cool for at least 5 minutes before slicing and serving.
Chicken pot pie is definitely at its best the same day, but if there are any leftovers, make sure to keep then in a covered container in the fridge. Eat within 2 days.