Preheat oven to 375°F (190°C).
Make the filling: In a large saucepan, melt butter over medium heat. Add flour, salt, pepper, and thyme. Whisk until smooth.
Add milk slowly, stirring constantly. Cook until thick and creamy (about 3–4 minutes).
Stir in chicken and frozen vegetables. Mix well and remove from heat.
Prepare the crust: Line a 9-inch pie dish with one crust. Pour in the filling. Cover with the second crust. Seal and crimp the edges. Cut 3–4 slits in the top to vent steam.
Brush with egg wash for a golden top.
Bake for 30–35 minutes or until crust is golden and filling is bubbling.
Cool for 10 minutes before serving.