Preheat the oven to 350°F. Line a baking sheet with parchment paper or a silicone baking mat.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large mixing bowl, beat the shortening and sugar until light and fluffy, about 3 minutes.
Add the egg and vanilla extract and continue beating until well combined.
With the mixer on low speed, alternately add the buttermilk and dry ingredients, beginning and ending with the buttermilk. Mix just until combined. The batter will be thick and soft, similar to muffin batter.
Scoop the dough onto the prepared baking sheet using about 3 tablespoons of batter per cookie, leaving 2 inches between each. If needed, use your finger or the back of a spoon to gently smooth the edges into a round shape.
Bake for 12–15 minutes, or until the edges are just beginning to turn golden. Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Frosting
Divide the softened butter evenly between two bowls. Add 1 cup confectioners' sugar to each bowl, then stir the cocoa powder into one of the bowls.
Using an electric mixer, beat each mixture until light and fluffy, about 2–3 minutes.
Add 1 tablespoon milk and ½ teaspoon vanilla extract to each bowl. Beat until smooth, adding a little extra milk if needed. The frosting should be thick but easy to spread.
Once the cookies are completely cool, frost half with vanilla frosting and the remaining half with chocolate frosting.
Storage
Store unfrosted cookies in an airtight container at room temperature for up to 4 days. Unfrosted cookies may also be frozen for up to 3 months. Thaw completely before frosting and serving.
Notes
Smooth any uneven edges before baking for the most uniform cookies.
A warm baking sheet can cause the second batch to bake more quickly, so begin checking for doneness about a minute earlier.
These cookies are best frosted the day they are served.