Preheat the oven to 350 degrees F (175 degrees C). Line cookie sheets with parchment paper.

Beat brown sugar and shortening together in a large bowl with an electric mixer until smooth. Beat in 1 egg, milk, and vanilla until smooth. Stir in molasses, baking soda, and cinnamon. Mix in flour until the dough is stiff enough to roll out.

Roll dough out on a lightly floured surface to 1/4 inch thickness. Cut into cookies using a pig-shaped cookie cutter. Place cookies 2 inches apart on the prepared baking sheets. Brush the tops of the cookies with beaten egg.

Bake in the preheated oven until risen and edges are lightly browned, about 15 to 17 minutes. Cool briefly on cookie sheets; serve warm or transfer to a wire rack to cool completely.