Heat a skillet over medium heat and melt the butter. Add the diced potatoes and fry for 15-20 minutes, stirring occasionally, until they turn crispy and golden. Season with salt and pepper.

Once your potatoes are beautifully golden, stir in the grated onion and fry for an additional minute. After one minute, remove the mixture from heat and let it cool slightly.

In a separate large bowl, combine the cooled potato-onion mixture with the grated cheese, Dijon mustard, chopped parsley, heavy cream, and any additional seasoning. Mix thoroughly.

Preheat your oven to 200°C (390°F) and roll out the chilled puff pastry. Cut the pastry into four rectangles and spoon a generous amount of filling onto one side of each rectangle. Brush edges with beaten egg, fold over, and crimp to seal.

Place the assembled pasties on a greaseproof tray lined with parchment paper. Brush tops with remaining beaten egg and bake for 15-20 minutes until golden-brown.