Heat 1-2 tbsp olive oil in a deep frying pan over high heat. Once hot, brown half the chicken pieces on both sides, season, and transfer to a plate or bowl. Repeat with the remaining chicken pieces.
Reduce the heat to medium and heat the remaining oil in the pan. Fry the onions, celery, and carrots for 8-10 mins stirring occasionally and scraping any browned bits from the base until all the vegetables have softened. Tip into the bowl with the chicken and return the pan to medium heat.
Melt the butter in the pan and stir in the flour to make a paste. Cook for a couple of minutes, stirring until the paste turns golden. Add a splash of the milk, then whisk to combine. Continue slowly adding the milk, whisking continuously until you have a smooth, creamy sauce.
Crumble the stock cube into the sauce and add 250ml water. Return to a gentle simmer, then return the chicken and veg to the pan. Stir in the mustard and thyme, and season well. Cover with a lid and simmer over low heat for 15-20 mins, stirring occasionally until the chicken is tender. Heat the oven to 400°F. Shred the chicken in the pan using two forks, pulling it into bite-sized pieces. Once completely cool, the filling will keep chilled for up to two days (providing the chicken is within its use-by date) or frozen for up to two months.
Transfer the filling to a pie dish (or divide it between individual pie dishes). Brush a little of the beaten egg around the rim of the dish. Unravel the pastry and lay it over the top of the dish, then trim the edges with kitchen scissors, leaving a little pastry overhanging the edge. Crimp this excess to seal the pie. Brush the pastry with more of the beaten egg and poke a few holes in the top using a skewer (this will release any steam inside during baking). Roll out any pastry offcuts and cut out decorations for the top if you like. Stick these to the pastry and brush with any remaining beaten egg. Bake for 35-40 mins until the pastry is golden brown and the filling is bubbling at the edge.