In a medium mixing bowl, whisk together the flour, cornstarch, baking powder & salt.
Throw the softened butter & sugar into the bowl of a stand mixer (w/ paddle attachment). Mix on medium-high for 3 to 5 minutes, until pale, light & super fluffy.
Add the beaten egg/milk & vanilla extract into the stand mixer bowl. Mix for another minute on medium-high.
Add the dry ingredients to the stand mixer bowl. Mix on slow JUST until combined into a smooth dough (be careful not to over-mix).
Lightly flour a piece of parchment paper & spoon half of the dough onto it. Form the dough into a ball & ~gently~ roll it out to about 1/4-inch thick. Set aside.
Repeat for the other half of dough, then sandwich a piece of plastic wrap between the two sheets, wrap it all in plastic & chill in the fridge for at least 1 to 2 hours (or up to two days).
Once ready, pre-heat the oven to 350°F & remove the two dough sheets from the fridge.
Line room-temp baking sheets with parchment paper & start cutting out the bats. Transfer each cookie onto one of the baking sheets, one to two inches apart.
Bake each sheet for 9 to 11 minutes until the cookies start to ~lightly~ brown around the edges (better to under- than over-bake them).
Remove the cookies from the oven & let them cool for a few minutes on the baking sheet. Then transfer each cookie onto a wire rack to fully cool.