In a large mixing bowl add the cake flour, all-purpose flour, baking powder, and cream of tartar. Whisk together then set aside.
In a large mixing bowl add the sugar, butter, and shortening. Use a hand mixer to beat together until light and fluffy. Add vanilla extract, almond extract, and the whole egg. Beat together until combined. Add egg white and continue beating until well combined. Turn off the mixer and use a rubber spatula to scrape the sides of the mixing bowl.
Turn the hand mixer on low and gradually add dry ingredients to wet ingredients. Mix until no flour pockets remain. Cover the mixing bowl with saran wrap and place in the refrigerator overnight.
Preheat the oven to 375 degrees and line 2 baking sheets with parchment paper. Set aside.
Remove cookie dough from the refrigerator and use a cookie scoop to create balls of dough, about the size of 2 to 3 tablespoons depending on how large you want your cookies. Place the balls of dough on the cookie sheet and use the bottom of a cup to flatten into a 1/2 inch thick round cookie. NOTE: An alternative method would be to roll the dough out on a flat surface to about 1/2 inch thick and then use a round cookie cutter to cut out the circles. Place 6 cookies on one baking sheet and 6 on another.
Place one cookie sheet in the oven and cook for 10 to 12 minutes. You want the edges to be firm without turning brown. Remove the baking sheet from the oven and immediately sprinkle sugar on the tops of the cookies.
Let the cookies cool 2 to 3 minutes on the baking sheet. Place the other baking sheet in the oven and cook for 8 minutes.
Repeat sugar and cooling steps for the second baking sheet.
Serve and enjoy!