Preheat your oven to 200°C/400°F/Gas Mark 6.
In a saucepan, add water and bring the diced potatoes to a boil. Cook until they are soft, about 10 minutes. Drain and let them cool.
In a bowl, mix the cooled potatoes with the chopped onion and grated cheddar cheese. Season with salt and pepper to taste.
Unroll the puff pastry sheet and cut it into 4 rectangles.
Spoon the cheese and potato mixture onto one half of each rectangle, leaving a border around the edge.
Brush the edges with beaten egg and fold the other half of the pastry over the filling. Press the edges together with a fork to seal.
Place the pasties onto a baking tray lined with parchment paper.
Brush the pasties with the remaining beaten egg.
Bake in the preheated oven for 25-30 minutes, until the pasties are golden brown and crispy.
Remove from the oven and let cool for a few minutes before serving.