Melt the butter in a saucepan over medium-low heat and cook and stir the onion with butter until translucent, about 5 minutes. Stir in the flour, salt and pepper to make a paste. Whisk in the chicken soup and milk; cook and stir the sauce until smooth and thickened, about 5 minutes. Lightly mix in the cooked chicken and mixed vegetables and pour the chicken and sauce into a 2-litre deep baking dish.
Unroll the shortcrust pastry sheet, lay it on the baking dish and fold and press the edges of the crust down to seal the pastry to the dish. Cut several small slits in the pastry.
Bake in the preheated oven until the pastry is golden brown and the filling is bubbling, 35 to 40 minutes. Cool 10 minutes before serving.