In a food processor, combine the flour, butter and 125g of the cheese. Pulse until a fine, sand like texture is achieved. Add the water and proccess until a soft dough has formed. Wrap and rest the dough in the fridge for at least 30 minutes.
In a medium sized saucepan, melt the butter and add the diced vegetables, cooking for 4-5 minutes until the vegetables start to soften. Add in the egg and the remainder of the cheese. Season with salt and pepper.
Roll the pastry out to a 3mm thickness and cut into 10cm rounds. Spoon a tablespoon of the vegetable mixture into the center of the dough and fold the pastry over, crimping the edges to seal the mixture inside.
Brush the pasties with an egg wash and bake in the oven for 20 minutes, until the pasties turn golden.