To the medium bowl, whisk together the all-purpose flour, sifted corn starch, powdered sugar and salt. Set aside.
To the bowl of a stand-up mixer (you can also use a medium bowl and an electric hand-mixer), add the butter and vanilla paste or extract. Beat until smooth. Next, add the egg yolk and mix just until incorporated.
Add all of the flour mixture and slowly mix it together (being sure not to go too quickly or else the flour will fly out of the bowl), until combined, about 1 minute.
Scoop the dough out of the bowl and form it into a ball. Place it in the center of a sheet of plastic wrap and press it into about a 2-inch round. Wrap it tightly in plastic wrap and transfer to the fridge to chill for about 1 hour.
Preheat the oven to 350 degrees F.
When it’s done resting, in the fridge, transfer the dough to the center of a sheet of parchment. Place a sheet of parchment on top and roll it out slowly. (If it’s too cold, let it come closer to room temperature, about 10 minutes.) Roll it out until it’s about 1/2 to 1/4-inch thick.
Using a 3-inch cookie cutter, stamp out cookies, having them as close to each other as possible. Transfer the cookies (I found it easiest to use an offset spatula to pick up the cookies) to a parchment-lined baking sheet, spacing them about 2-inches apart. Transfer to the fridge to chill for about 10 minutes. Repeat until you work your way through all of the dough. I rerolled the dough about 2 more times.
Score the tops of the cookies with a tines of a fork. Transfer to the oven to bake for about 11 to 13 minutes, until the cookies are a bit firm to the touch but have zero color on the edges. These cookies are baked just until set. Allow to cool on the baking sheets until room temperature.