In a large pan over medium heat, melt butter and add diced potatoes. Fry until crispy and golden brown, about 15-20 minutes. Season with salt and pepper to enhance flavor.

Stir in the grated onions and fry for an additional minute until softened, then remove the pan from heat and allow the mixture to cool slightly.

In a mixing bowl, combine the cooled potato-onion mixture with freshly grated cheese, Dijon mustard, chopped parsley, heavy cream, and any extra seasonings you like. Stir until well blended.

Roll out your chilled puff pastry and cut it into 4 rectangles. Place a generous amount of filling on one side of each rectangle, brush the edges with beaten egg to seal, fold over, and crimp the edges with a fork. Cut small steam holes on the top.

Arrange the pasties on a greaseproof baking tray, brush with more egg wash, and pop them into a preheated oven at 200°C (390°F). Bake for 15-20 minutes, or until they are beautifully golden and flaky.