Heat oven to 375ºF. Line 4 half-sheet pans with parchment paper and set aside.
Combine the shortening, sugar, and brown sugar in the work bowl of a stand mixer fitted with the paddle attachment. Cream together on high speed until light and fluffy, 3 to 4 minutes. Sift together the cake flour, salt, and baking powder in a medium mixing bowl and set aside.
Add the eggs, one at a time, to the creamed mixture, increasing the speed between each addition. Then add the vanilla. Increase the speed to high until thoroughly incorporated.
Decrease the speed to low and add the dry ingredients to the mixer in three installments. Be sure to stop the mixture and scrape down the sides of the work bowl between each addition. Stir in the chocolate chips.
Chill the dough completely, approximately 1 hour. Scoop the dough into 1 1/2 ounce portions onto the prepared half-sheet pans, 6 cookies per sheet. For most even doneness, bake one sheet at a time for 13 minutes, rotating the pan halfway through. Bake two pans at a time for 14 minutes, checking the cookies after 5 minutes. Rotate the half-sheet pans for more even browning.
Move the finished cookies to a wire rack. Cool completely and store in an airtight container.