Weigh or measure the sugar into a bowl and set it aside. In another bowl, weigh or measure the flour. Add to the flour the cocoa powder, baking powder, and the salt. I run a whisk through to blend.
Cube the butter into the mixer bowl and mix on a medium mixer speed for about 2 minutes or until it looks creamy. Now, add the sugar and mix for about 3 minutes. This depends on how cold your butter was, so 3 minutes at least. Next, add the egg and the vanilla extract and mix until incorporated.
Scrape down the bowl and on a medium low mixer speed add about ⅓ of the flour mix at a time. It will look dry! Finally, add the mini chocolate mint chips and mix for about 5 seconds. The cookie dough will be stiff but will all come together.
Place all the cookie dough and crumbs (there will be some) onto a pastry mat or counter. You want to knead the cookie dough and disperse the mini chocolate mint chips evenly throughout the cookie dough. Roll it into a log and divide it into 2 halves. Flatten each half and wrap each in plastic wrap. Chill for 30 minutes.
Preheat the oven to 350°F (175°C or 180°C). I use powdered sugar to dust my pastry mat. My rolling pin has bands on the ends to determine the thickness of the cookie dough I am rolling out. I did ¼ inch bands. Line 2 cookie sheet pans with parchment paper.
Unwrap one of the flattened cookie dough disks and put it on the pastry mat, let it warm up before rolling it out. Use your cookie cutter for as many cutouts as you can and ball the cookie dough back up and roll it out again. Do this until all the cookie dough is used. I added 11 cutout cookie dough onto a sheet pan. Bake for 9-11 minutes. I leave them on the cookie sheet pan for at least 5 minutes to cool down some before moving them to a cooling rack. If you move them too soon, some of the cutout shamrock leaves or the stem could break off.