In a medium skillet, melt the butter over medium heat. Add the diced white potato and fry for about 15 to 20 minutes, stirring occasionally, until golden and tender. Season with salt and pepper to taste.

Once the potatoes are golden, stir in the grated onion, cooking for an additional minute until softened. Remove from heat and let cool slightly.

In a mixing bowl, combine the cooled potato-onion mixture with sharp cheddar cheese, Dijon mustard, and heavy cream. Mix until well blended. Fold in the parsley if using.

On a floured surface, roll out the chilled puff pastry and cut it into four rectangles. Place a generous amount of filling on one side of each rectangle. Brush edges with beaten egg, fold, and crimp to seal.

Preheat the oven to 200°C (390°F). Place pasties on a baking tray lined with parchment and brush the tops with beaten egg. Bake for 15 to 20 minutes until puffed and golden brown.