Preheat the oven to 190°C.
Heat the olive oil in a large, heavy-based saucepan over a medium heat and sweat the onion and carrot for 5-6 minutes, stirring occasionally, until softened. Increase the heat a little and add the mushrooms with a little seasoning.
Continue to cook, stirring from time to time, until the mushrooms have softened. Add the mince and brown all over for 5-6 minutes. Pour in the stock, bring the mixture to the boil then reduce to a simmer for 10-15 minutes until most of the stock has evaporated. Remove from the heat, adjust the seasoning and stir in the chopped parsley. Set to one side to cool.
Roll half the pastry out on a lightly floured surface to ½cm thickness. Cut four rounds of pastry slightly larger than the diameter of an 8cm individual fluted tart tin. Line the tins with the pastry, pressing in well. Prick the bases and chill. Roll the other half of pastry out to ½cm thickness and cut 4 rounds of pastry to act as lids for the pies.
Once the meat mixture has cooled, drain away the excess liquid and spoon into the pastry cases. Top the meat mixture with the pastry lids, sealing well around the edges onto the pastry base. Brush with the beaten egg and bake for 18-22 minutes until the pastry is cooked and lightly coloured on top.
Remove and allow to cool slightly on a wire rack before serving.
For top tips on protecting you and your family when preparing raw meat and poultry, visit Food Safety in the Home and view the full Food safety at home video.