Peel and finely chop the onion and garlic. Finely chop the carrots and celery.
Put the vegetable oil in a large pan over a medium heat. Add the onion, carrots and celery and cook for 5 minutes.
Add the mince and garlic - cook until the mince is browned. Stir in the flour, then add the beef stock, Worcestershire sauce, salt and pepper. Bring to a simmer and cook for 10 minutes until the sauce is very thick. Add the peas, stir and take off the heat. Allow to cool.
Preheat the oven to 200 degrees Celsius. Unroll the pastry sheets and cut each one into 8 even squares. Put a tablespoon of the beef filling in the middle of one of the pastry squares, then pinch the pastry closed around it. Put on a baking tray and repeat with the rest of the pastry.
Beat the egg and brush each tartlet with the egg. Put in the oven and cook for 20-30 minutes until golden brown.