In a large skillet, heat 2 tablespoons of butter or oil over medium heat. Add the diced white potatoes and cook for about 15-20 minutes, stirring occasionally, until they are golden and crispy on the outside yet tender on the inside. Season with salt and pepper, then transfer to a bowl to cool slightly.

In the same skillet, melt an additional tablespoon of butter. Add the grated onion, cooking for about 1 minute until softened and fragrant. Combine the cooked onion with the cooled potatoes, stirring well.

In a mixing bowl, combine the potato and onion mixture with the sharp cheddar cheese, Dijon mustard, and heavy cream. Add chopped fresh parsley, along with salt and pepper to taste. Stir until well mixed.

Preheat your oven to 200°C (390°F). Roll out the puff pastry on a floured surface and divide it into four rectangles. Spoon the filling onto one side of each rectangle, leaving room at the edges for sealing. Brush the edges with beaten egg.

Fold the pastry over the filling to create a pocket and crimp the edges with a fork to seal. Place the pasties on a greaseproof tray, brush the tops with more beaten egg, and make small steam holes. Bake for 15-20 minutes until golden brown and flaky.