In a medium saucepan, combine the cranberries, sugar, water, and lemon juice. Bring to a boil over medium heat, stirring occasionally until cranberries start to burst, about 5-7 minutes.

Mix cornstarch with a little cold water until smooth. Stir into the pot with the cranberry mixture. Cook for another 2-3 minutes until thickened. Remove from heat and let cool.

Preheat your oven to 375°F (190°C).

Roll out the pie dough on a floured surface. Cut out small circles or squares, about 4 inches in diameter.

Place a spoonful of cooled filling in the center of each dough circle. Be careful not to overfill.

Fold the dough over to create a half-moon shape. Press edges with a fork to seal.

In a small bowl, beat the egg with milk. Brush over the pies for a golden finish.

Place pies on a baking sheet lined with parchment paper. Bake for 20-25 minutes or until golden brown.

Let pies cool on a wire rack. Serve warm or at room temperature.