In a large mixing bowl add the cake flour, all-purpose flour, baking powder, cream of tartar and salt. Whisk together then set aside.
In a separate large mixing bowl, beat together the butter, sugar, and the whole egg. Beat until well combined, scraping down sides of the bowl.
Add in the egg white and beat until combined. Again, scraping down sides of the bowl.
Add in shortening and vanilla and beat until light and fluffy (about 2 minutes). Scrape down the sides of the bowl.
Slowly add dry ingredients into wet ingredients. Beat just until mixed. Do not overmix.
Cover bowl with plastic food wrap and place in the fridge overnight.
Remove bowl from fridge and lay dough out on silicone mat. Using a rolling pin, roll out dough to ½-inch thickness. Cut into large circles (3-inch size) using a cookie cutter.
Place unbaked circle cookies onto a baking sheet and put back into the refrigerator (uncovered) for another hour.
Preheat the oven to 375°F. Line two baking sheets with silicone baking mats. Place cookies at least two inches apart on baking sheets.
Only bake one tray at a time. Place the first cookie sheet into the oven and bake for 10-12 minutes until the middle tops of the cookies no longer look wet and the bottom of the cookies look slightly brown. Then bake the second tray.
Let the cookies cool on baking sheets 2 to 3 minutes before removing to a wire rack to cool completely. The cookies should be completely cooled before adding frosting.
To make the frosting, place all frosting ingredients (butter, confectioners sugar and vanilla) in a mixing bowl and beat on high until light and fluffy (about 5 minutes).
Frost tops of cookies and top with Halloween sprinkles. Store in a covered food storage container in the fridge for 4 to 6 days.