Make the Crust

1. Combine the flour and salt in a medium bowl. Add the butter and shortening, then use a pastry cutter or fork to break down the fat until it becomes the size of peas. Pour in 6 tablespoons of water and mix gently with a rubber spatula or wooden spoon until the dough just starts to form a shaggy mass. Add more water one tablespoon at a time if needed. Use your hands to press the dough until it just comes together. Resist the urge to knead and squish - overmixing will make it tough. The dough should not be sticky, and you should be able to see tiny pieces of butter and shortening flecked throughout.
2. Once the dough has formed, split it into two balls, then gently shape them each into discs. It's important to shape them now so they roll out round later. Wrap in plastic and refrigerate for a minimum of 30 minutes (or up to two days). For longer storage, wrap tightly and freeze for up to 6 months.

Make the Filling

1. Melt the butter in a large heavy bottomed pot, then add in the onion, carrots and celery. Season with salt and pepper, then cook, stirring occasionally until the onions turn translucent, about 5 minutes. Add in the garlic, and cook for 2 minutes more. Sprinkle the flour over top, then stir until everything is evenly coated and all the flour is moistened. Pour in the chicken stock and apple cider while stirring, and cook for about 10 minutes until the mixture has thickened. Stir in the heavy cream and thyme, then remove from the heat. Taste and adjust the seasoning as needed. Stir in the chicken, peas and parsley, then allow to cool completely until proceeding with the recipe. Pouring a hot filling into the crust will make the dough difficult to work with and will not bake up as well.

Assemble and Bake

1. Preheat the oven to 350 degrees.
2. When the dough has rested and chilled, remove one disc at a time, unwrap and place on a generously floured work surface. Dust a rolling pin with flour, and begin to roll out the dough, making sure to constantly rotate it. This will help ensure the dough doesn't stick to the counter, and also will help keep it round. Use a measuring tape or the pie plate to determine when the dough has reached the right circumference. If the dough does not roll out perfectly round, use a knife or a pizza cutter to trim the edges to even it out.
3. Gently roll the dough onto the rolling pin and use it to transfer to a pie plate, then press it in to fit. Pour the cooled filling into the crust, then go around and lightly dab the top edges of the exposed dough with water.
4. Remove the second disc of dough from the fridge, then roll it out the same way and use the rolling pin to transfer it over top of the filling. Use your fingers to pinch together the edges of the top and bottom crust to seal in the filling, then use a pair of kitchen shears to snip off any excess, leaving about 1 inch of overhang. Tuck and roll the overhang under, then use your fingers or a fork to crimp the edges. Gently cut a few slits to vent the top, then use a pastry brush to coat the entire thing with the beaten egg. Place the pie on a foil lined baking sheet to catch any drippings, and bake in the oven for approximately 1 hour. It will be ready when the crust is golden brown and the filling is bubbling inside. Remove from the oven and allow to cool for 30 minutes before cutting.