In a large mixing bowl, whisk together the cake flour, all-purpose flour, baking powder and cream of tartar. Set it aside.
Using a stand mixer, or a large mixing bowl and a handheld mixer on medium-high speed, beat together the softened butter, butter flavored shortening and granulated sugar for 1½ to 2 minutes until the mixture is light and fluffy.
Reduce the mixer speed to medium. Add the large whole egg and vanilla extract. Beat just until the egg is incorporated.
Add the large egg white and mix until well combined.
Slowly add in the flour mixture and mix just until the flour is incorporated and smooth. Cover tightly and chill in the refrigerator overnight, or for at least 10 hours.
Preheat the oven to 375°F. Line 2 baking sheet with parchment paper.
Lightly flour your working surface with flour.
Divide the cookie dough in half. Lightly flour the top of the dough.
Using a rolling pin, carefully roll the dough out to ¼ inch to ⅜ inch.
Lightly flour the edges of the gingerbread man cookie cutter and cut your cookies.
Evenly space the gingerbread men 6 per baking sheet.
Bake for 10 minutes. The edges should not brown at all.
Remove the cookies and allow them to rest until they are completely cooled. While they are cooling, make the icing.