Preheat the oven to 350°F (177°C). Line two large baking sheets with parchment paper or silicone baking mats and set aside.
In a mixing bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large mixing bowl using an electric mixer, cream the shortening and sugar together for 1 to 2 minutes or until well combined. Mix in the egg, milk, and vanilla extract until fully combined, making sure to stop and scrape down the sides of the bowl as needed.
Add the dry ingredients and mix until fully combined. The mixture will be a little crumbly at first but it will come together as you continue mixing it. Once the dough comes together, use your hands to form it into a ball.
Divide the dough in half. Lightly flour a piece of parchment paper, add half of the dough, top with another piece of parchment paper, and roll the dough out ¼-inch thick between both pieces of parchment paper. Repeat with the other half of the dough between two separate pieces of parchment paper. This dough doesn't require any dough chilling, but if you prefer colder dough so that it's easier to work with you can place both pieces of rolled out dough between the parchment paper on a baking sheet and refrigerate for 30 minutes to one hour.
Peel off the top layer of parchment paper. Using 2.5 to 3 inch cookie cutters, cut the cookie dough into shapes and place them onto the prepared baking sheets, making sure to leave a little room between each one. If needed, flour a thin spatula and use that to transfer the cut out cookies to the baking sheet. Re-roll any scrap pieces of dough between the parchment paper and continue cutting out shapes. Repeat with the other sheet of cookie dough.
Bake for 9 to 12 minutes or until the tops of the cookies are set the bottom edges are lightly browned.
Cool on the baking sheets for 5 to 10 minutes, then transfer to a wire rack to finish cooling.