Preheat the oven to 350 degrees F.
Cut the VERY cold (right out of fridge) butter with a knife into 1-inch cubes. Place in the stand mixer with the sugar. Beat until completely creamy and light.
Add in the egg, Mexican vanilla extract, almond extract, and orange extract. Beat until completely combined.
Add in the cornstarch, baking powder, and 1 cup of flour. Beat until completely combined scraping the edges as needed. Add in the next cup and beat until a dough forms. Add in the final 3/4 cup adding an additional 1/4 cup as needed for a dough that is firm enough to be cut out into shapes (or a circle).
If the dough looks crumbly, keep beating until a dough does form (it will form even though it looks like straight crumbles!!) and if needed knead it with your hands. Just be careful to not overwork the dough as that leads to tough cookies.
In between two sheets of plastic wrap or parchment paper, roll out the dough to about 1/2" thickness. Cut out the cookies and place on a parchment or silicone lined tray. Chill for 30 minutes.
Bake for 12-14 minutes watching carefully for when they slightly brown at the edges/bottom. Be careful to not overbake - the center should still look soft and not be brown at all. Under-baking slightly is huge for the flavor and texture of these cookies.
Allow to cool on a cooling rack for about 2 minutes. Then place the cookies in a single layer (or separated with wax paper) in a large re-sealable bag. Seal the bag to keep the moisture in and the cookies ultra soft. Remove when cooled and ready to frost.