Cut circles in whatever size you would like your pasties to end up. Remember the circle will be folded in half so allow for this when cutting. Large coffee mugs make a good mini-pastie size for finger foods.
Put a few tablespoons of the mince mixture on one half of the pastry and sprinkle with a little cheese. Leave a 1cm clear space clear around the mixture. Don't overfill the pastry or it will end up bursting when cooking. Using a pastry brush, brush a little beaten egg on the 1cm space and fold the pastry over so the edges meet. Using your finger or a fork, press the edges together to seal.
Bake at 200 degrees for 20 minutes or until pastry is golden.