Heat oil in a large saucepan over medium heat. Add leeks, celery, carrot and potato. Cook, stirring occasionally, 5 minutes. Add mushrooms. Cook, stirring occasionally, 5 minutes. Stir in flour, thyme and salt until blended. Stir in stock. Increase heat to medium-high. Cook, stirring, until thickened, 2 minutes. Stir in chicken and peas. Transfer to 23 cm or 25 cm deep pie plate. Let cool to room temperature.
Preheat oven to 200°C. Unfold pastry, checking its fit on top of pie plate. Brush underside of pastry with glaze; place over filling. Trim edge of pastry; crimp or mark decoratively with a fork, if desired. Brush top with glaze. Cut four 2.5 cm slits in the centre to allow steam to escape.
Bake until filling is bubbling and pastry is golden brown, 25 to 30 minutes. Let stand at least 10 minutes before serving.