In a large bowl, whisk together the flour and salt. Add the chilled, cubed butter and use a pastry cutter or your fingertips to work the butter into the flour until the mixture resembles coarse crumbs.
Gradually add the cold water, 1 tablespoon at a time, stirring with a fork until the dough comes together. Form the dough into a ball, then flatten it into two disks.
In a large skillet or Dutch oven, melt the butter over medium heat. Add the chopped onion and sauté for about 4-5 minutes until soft and translucent.
Add the chopped potatoes and carrots to the skillet and cook for about 5 minutes, stirring occasionally.
Stir in the minced garlic and curry powder, cooking for another 1-2 minutes until the spices are fragrant.
Add the chopped chicken, chicken broth, and mushrooms. Bring the mixture to a simmer and cook for 10-12 minutes, or until the vegetables are tender and the flavors are well combined.
Add the green peas, salt, and black pepper. In a separate bowl, combine the cornstarch with water to form a slurry. Incorporate this slurry into the filling, mixing thoroughly. Keep cooking for another 2-3 minutes until the mixture has thickened. Remove from heat and allow the filling to cool for a bit.
Preheat your oven to 400°F (200°C).
On a lightly floured surface, roll out one of the chilled pie dough disks into a circle large enough to fit a 9-inch pie dish. Gently press the dough into the bottom and up the sides of the pie dish, leaving some overhang.
Spoon the slightly cooled filling into the pie crust, spreading it evenly.
Roll out the second dough disk into a circle large enough to cover the top of the pie. Place it over the filling, trimming any excess. Pinch the edges together to seal and crimp as desired. Cut a few small slits in the top of the crust to allow steam to escape.
In a small bowl, whisk together the egg and water. Brush the top of the pie with the egg wash for a beautiful golden-brown finish.
Place the pie on a baking sheet to catch any drips and bake in the preheated oven for 35-40 minutes, or until the crust is golden brown and the filling is bubbling.
Allow the pie to cool for about 10 minutes before slicing and serving. Enjoy this warm, comforting, and flavorful curry pot pie with a side salad or steamed vegetables.