Sift flour, cornstarch, baking powder and salt into a large bowl. Whisk to blend. Set aside.
In the bowl of an electric stand mixer, on medium speed, whip together butter, shortening and sugar until very pale and fluffy, about 4 minutes, scrapping down the sides of the bowl as needed.
Add the egg and mix to combine.
Add the egg white, vanilla and almond extract and mix until well combined.
With the mixer running on the lowest setting, slowly add in dry ingredients and mix just until combined.
Transfer dough to an airtight container and refrigerate 1 1/2 - 2 hours or until the dough is firm. (I refrigerated the dough overnight because that is what worked best for my schedule.)
When ready to bake, preheat oven to 375. Prepare cookie pans by either using a Silpat or parchment paper. Set aside.
While the oven is heating, sprinkle a clean work surface with cake flour. Turn out half of the dough onto the work surface. Lightly sprinkle the surface of the dough with cake flour.
Evenly roll dough out to a generous 1/4-inch thickness (that means bigger than 1/4-inch but less than 1/2-inch ;) ), or up to 1/2-inch for thicker cookies. (The pictured cookies were about 1/2-inch in thickness because I ate all of the thinner ones. Yum.)
Cut into desired shapes. (I used a medium heart cookie cutter and got 20 cookies).
Transfer to Silpat or parchment paper lined baking sheets. Bake in preheated oven 8 - 11 minutes ( The cookies should be a pale color, not brown. Overcooking will cause a crispy cookie, which totally defeats the purpose of a soft cookie, right? ).
Remove from oven and allow to cool on baking sheet several minutes before transferring to wire rack to cool.
Repeat the cookie process with the remainder of the cookie dough and as much of the dough scraps as you can use. The cookies that are made out of the dough scraps will still taste very good, but they may not be as soft as the cookies which were cut from the first pass.
Cool completely then frost with Vanilla Frosting and add sprinkles if desired. If using sprinkles, be sure to sprinkle immediately after frosting each cookie so that the sprinkles will stick before the frosting sets.
Store in an airtight container at room temperature.