Preheat oven to 350˚F (180˚C). Line two baking sheets with parchment or lightly grease.
In a large bowl, whisk together the all-purpose flour, cake flour, baking powder, baking soda, and salt.
In another large bowl, beat together the butter and sugar until light and fluffy, about 2 minutes. Beat in the eggs, one at a time, just until blended.
Stir in 1/3rd of the flour mixture into the egg mixture, followed by 1/2 of the buttermilk. Add another 1/3rd of the flour mixture followed by the remaining buttermilk, and then the remaining flour, adding each just until blended with no streaks. Stir in the vanilla extract and lemon zest.
Use a 1/4 cup (60 milliliters) ice cream scoop to place mounds of dough, in as even a circle as possible, on the prepared baking sheets, 3 inches (7.5 cm) apart (about 6 cookies per baking sheet).
Bake, 1 sheet at a time, in preheated oven until cooked through and slightly golden, about 15-17 minutes. Allow to cool for 5 minutes before removing to wire rack.
Repeat with remaining dough (make sure the baking sheet is completely cool before adding more dough). Allow the cookies to cool completely before topping with the glaze.