Add the eggs to a large bowl. Using a hand mixer on medium speed, beat the eggs on high speed until light and foamy, about 5 minutes; set aside.
In another large bowl, combine 5 cups of the flour, confectioners’ sugar, and baking powder. Stir with a whisk to combine. Set aside.
On low speed, gradually beat in the vegetable shortening and extracts until the mixture resembles fine crumbs. Gradually add the beaten eggs.
Add the flour mixture to the egg mixture 1 cup at a time, mixing well after each addition. The dough should be stiff. If it is not stiff enough to roll into a cookie ball, gradually add more flour beginning with ½ cup. (This is where the extra cup of flour comes in). If still not stiff enough, gradually add remaining half cup. By this time the cookie dough should be stiff enough to shape into a cookie ball.
Roll the dough into 1-inch balls. Place the cookies at least 2 inches apart on a baking sheet lined with parchment paper.
Bake at 350 for 12-14 minutes. The top of the cookies will not brown, but bottoms should brown slightly.
To Glaze The Cookies
In a small bowl, combine the confectioner’s sugar, milk and extracts until smooth.
As soon as cookies are removed from the oven, quickly dip two or three times into the glaze.
Place on a wire rack with wax paper beneath it to drain and immediately top with sprinkles. Let dry 24 hours. Place in airtight containers to store.