In a large frying pan sauté finely diced onion in olive oil on a low heat while you prepare the other vegetables.
Finely dice the potato, carrot, and pumpkin into ½ cm cubes. Add to the onion and cook for 10 minutes or until slightly soft. Remove from heat and stir through grated cheese.
Defrost sheets of pastry or roll out pastry if using a block or a roll. For mini pasties cut out 4 x 12cm rounds per sheet of puff pastry or for large pasties cut out 8, 21cm rounds. Preheat oven to 200 degrees Celsius.
Place a generous tablespoon of pasty mixture in the centre of each round or for divide the mixture evenly between these and follow the same method as outlined for the mini pasties. Paint the edge of the circle with egg. To seal gently fold circle in half to join the edges. Press together with your fingers to create a frill at the top.
Place on a tray lined with baking paper. Brush with egg and sprinkle with sesame seeds. Bake for 20-25 minutes or until golden.