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 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 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 for 2-3 hours.
Preheat the oven to 375 degrees and line 2 baking sheets with parchment paper. Set aside.
Remove cookie dough from the refrigerator and roll the dough out on a flat surface to about ½ inch thick. Cut out desired shapes with floured cookie cutters. Place 6 cookies on one baking sheet, and 6 on another.
Place one cookie sheet in the oven at a time and cook for 10-12 minutes. You want the edges to be firm without turning brown. Let the cookies cool 2-3 minutes on the baking sheet. Place the other baking sheet in the oven and cook.
In a medium mixing bowl, beat together 1 cup butter and 4 cups powdered sugar. With the beater turned on, drizzle heavy cream into butter/sugar mixture and beat until fluffy. Add more cream to thin out frosting to desired spreadable consistency. Spread frosting onto cooled cookies and decorate with sprinkles.
Store unfrosted cookies in an airtight container for up to 5 days or freeze up to 3 months.
Store frosting in the refrigerator up to two weeks or freeze up to 3 months.
Store decorated cookies in an airtight container in the refrigerator for up to 1 week.
Use clear imitation vanilla for a whiter frosting. You can also substitute in shortening for a portion of the butter for a whiter frosting.
Use a bit of gel food coloring to make colored icing.
Add sprinkles right away as the frosting dries a bit on the surface after a few minutes and they won’t stick as well.