In a small bowl, whisk together the cake flour, baking soda, salt, and cocoa powder.
In a stand mixer fitted with the paddle attachment, mix the butter, confectioners’ sugar, vanilla, and the flour mixture on medium-low speed until evenly mixed, 1 to 2 minutes.
Shape the dough into approximately 1 1/4 x 2 x 7-inch rectangle*. Wrap in plastic, refrigerate until firm, at least an hour. It can also be made the day before or frozen for several weeks. Slice into 1/8-inch-thick cookies.
Preheat the oven to 350°F / 175°C with the rack in the middle of the oven.
Place the sliced cookie dough on two doubled up baking sheets lined with parchment. Separate by about 1 inch to allow for spreading.
Bake for about 10 minutes or until the cookies are set and dry looking.
Allow to cool completely before assembling the ice cream sandwich bars.