Combine butter and sugar in a large bowl and use an electric mixer to beat until creamy and well-combined.
Add egg and vanilla extract and beat well.
In a separate bowl, whisk together flour, cocoa powder, baking powder, and salt.
Gradually add dry ingredients into wet until completely combined.
Lay out a large piece of plastic wrap and transfer half of the dough onto the wrap -- it will be pretty sticky!
Cover with clear wrap and mold into a disk. Repeat with remaining cookie dough in a separate piece of cling wrap. Transfer cookie dough to the refrigerator and chill for at least 2-3 hours.
Once dough has chilled, preheat your oven to 350F (175C) and line a baking sheet with parchment paper. Set aside.
Generously dust a clean surface with flour and place one unwrapped cookie dough disk onto the surface. Lightly flour the dough and roll out to ⅛" (for thinner, crispier cookies) or ¼" (for thicker, softer cookies). Continue to add flour as needed both on top of and beneath the dough so that it doesn't stick.
Use cookie cutters to cut out shapes and use a spatula to transfer shapes to prepared baking sheet. If you don't intend to frost your cookies with the icing listed below, you can instead sprinkle them with sanding sugar at this point (before baking).
Bake on 350F (175C) for 9-11 minutes (may need more time for larger or thicker cookies, or less for smaller or thinner ones).
Allow cookies to cool completely on cookie sheet before moving and frosting.
Sugar Cookie Frosting
Combine sugar, 2 Tablespoons of milk, corn syrup, and vanilla extract in a medium-sized bowl and stir until combined. If your frosting seems too thick, add more milk, about a teaspoon at a time, until the frosting is thick but pipeable. If you accidentally add too much milk, add powdered sugar until desired texture is reached.
If coloring the frosting, divide into bowls and color as desired at this point.
Transfer frosting to a piping bag with a piping tip (I used Wilton 5), or place in a Ziploc bag and snip a small piece of the corner off (this technique is not as neat, but this will still work, just take care that the frosting isn’t so thick that it breaks open the seam of the bag when you are squeezing).
Pipe frosting on cookies and decorate with sprinkles, if desired.
Allow frosting to harden before enjoying (this usually takes several hours)
Store uneaten cookies in an airtight container at room temperature.
*Yield varies greatly depending both on how thick you roll the dough and the size of the cookie cutters that you use. This recipe can be doubled.**You may also cut the vanilla extract down to ¾ teaspoon and add ¼-1/2 teaspoons of either almond or lemon extract (or just about any other extract you'd like!) My cookie cutters were about 3" in length, if you're using smaller cookie cutters you will need to bake for less time, keep an eye on the edges of your cookies to know when they are done.