Combine the flour, baking powder, and salt in a small bowl. Set aside for use in Step 4.
Using an electric mixer fitted with a paddle attachment, beat the butter and shortening on medium speed until creamy.
Gradually add the sugar and beat until light and fluffy, about 1 minute. Do not over mix, or your cookies will dome upon baking, making them more difficult to decorate later.
Whisk together the egg, milk, and vanilla extract in another bowl.
Slowly blend into the butter mixture on low to medium speed and mix until smooth. Scrape down the sides of the bowl, as needed, to ensure even mixing.
Turn the mixer to low speed and gradually add the reserved dry ingredients, mixing until just incorporated.
Flatten the dough into a disk, wrap tightly in plastic, and refrigerate about 3 hours, or until firm enough to roll without sticking.
Position a rack in the center of the oven and preheat the oven to 375°F. Line 2 cookie sheets with parchment paper (or silicone baking mats) and set aside.
On a lightly floured surface, roll the dough to a 1?8- to 3?16-inch thickness. (Note: It's best to roll these cookies no thicker than 3?16 inch in order to keep them their flattest for decorating.)
Cut out assorted shapes with your favorite cookie cutters or the cutters or templates specified in the project you've chosen. Carefully transfer the cookies to the prepared cookie sheets with an offset spatula, leaving no less than 3?4 inch between each cutout.
Baking time will vary considerably with cookie size and thickness. Bake until the cookies are lightly browned around their edges, about 8 to 10 minutes for 2 1?2-inch round cookies or as specified in your project. Let particularly long or delicately shaped cookies cool 1 to 2 minutes on the cookie sheets before transferring to wire racks. Otherwise, immediately transfer to racks and cool completely before frosting and/or assembling with Royal Icing or decorating.
Notes
For easiest handling, the dough should be chilled about 3 hours before rolling and cutting.
The dough can be frozen for 1 month or more with minimal loss of flavor if wrapped tightly in plastic and then foil.
For best eating, store baked cookies in airtight containers at room temperature and enjoy within 7 to 10 days.
Recipe yields 1 pound 6 ounces dough or 36 to 40 (2 1/2-inch) round cookies