Preheat your oven to 190°C (375°F) and grease a 12-hole muffin tin.
In a large mixing bowl, combine the plain flour, Tate & Lyle granulated sugar, and salt. Add the cubed butter and rub it into the flour mixture using your fingertips until it resembles breadcrumbs.
Make a well in the center of the mixture and add the beaten egg and cold water. Mix with a fork until the dough comes together. Gather the dough into a ball, wrap it in cling film, and refrigerate for 30 minutes.
In the meantime, prepare the filling. In a saucepan, combine the diced apples, Tate & Lyle light brown soft sugar, ground cinnamon, ground nutmeg, and lemon juice. Cook over medium heat for about 5 minutes until the apples have softened slightly. Remove from heat and let it cool.
Take the chilled dough out of the refrigerator and roll it out on a lightly floured surface to a thickness of about 3mm. Cut out circles slightly larger than the holes in the muffin tin.
Line each hole of the muffin tin with a circle of dough, pressing it gently into the sides. Fill each pastry case with the cooled apple filling.
Sprinkle a little Tate & Lyle demerara sugar over the top of each mini pie for a crunchy topping.
Bake in the preheated oven for about 15-20 minutes or until the pastry is golden brown and the filling is bubbling.
Remove from the oven and let the mini apple pies cool in the tin for a few minutes. Carefully transfer them to a wire rack to cool completely.
Serve the mini apple pies warm or at room temperature. Enjoy!