Preheat the oven to 375°F (190°C). In a mixing bowl, combine flour and cold butter until crumbly.

In another bowl, whisk together the egg and milk. Gradually add to the flour mixture, stirring until the dough forms.

Roll out half the dough on a floured surface to about 1/8 inch thick; cut into rectangles (3 x 4 inches).

Mix brown sugar and cinnamon in a small bowl. Spoon about 1 tablespoon onto half of the rectangles.

Cover with remaining rectangles, press edges to seal, and crimp with a fork.

Bake on a parchment-lined sheet for 20-25 minutes until golden. Cool slightly before frosting.