Trim any fat or gristle from the meat and cut it up into very small pieces.
Place in a large bowl and add the diced onion, carrots, potato and celery. Mix well and season with salt and freshly ground pepper.
Preheat oven to 350ºF.
Cut preferred shape of pie bottoms and tops. I did heart shapes and was able to get 8 small pies and 6 large pies. Divide the meat and vegetable mixture between the bottoms, pilling it in the middle of each.
Lay the tops over the bottom and pile and pinch edges together by pleating or using a fork.
Make a small hole in the top of each pie to let out the steam.
Brush with beaten egg and slide the pies on to baking sheets.
Bake in preheated oven for an hour.
Serve hot or cold.