Preheat oven to 450°F (230°C).
Melt butter in large saucepan over medium heat. Add flour and cook, stirring constantly, until a blonde roux is made, 1 to 2 minutes. Slowly stir in stock (or broth) and heavy cream, then bring to boil over medium-high heat.
Stir in potato and thyme. Reduce heat to medium and simmer until sauce is thickened and potato is tender, about 8 minutes. Remove from heat and stir in chicken and frozen vegetables.
Remove the dough lined pie pan from the fridge and unwrap.
Transfer filling to dough-lined pie pan. Loosely roll remaining dough round around rolling pin and gently unroll it onto filling. Trim overhang to 1/2 inch beyond lip of plate, using kitchen scissors or a sharp knife.
Pinch edges of top and bottom crusts firmly together. Tuck overhang under itself; folded edge should be flush with edge of plate. Crimp dough evenly around edge of plate using your fingers(see video). Cut four 2-inch slits in top of dough, approximately equal distant from each other.
Using a pastry brush, brush top of pie with beaten egg.
Place pie on rimmed baking sheet and bake until top is light golden brown, 18 to 20 minutes. Reduce oven temperature to 375°F (190°C), rotate sheet, and continue to bake until crust is deep golden brown, 12 to 15 minutes longer. Let pie cool on wire rack for at least 45 minutes. Slice and serve.
Enjoy!