Preheat the oven to 450°F. Line a baking sheet with parchment paper and set aside.
Add the all-purpose flour, cake flour, sugar, baking powder, salt, and baking soda to the bowl of a food processor. Pulse a few times to combine. Add the frozen cream cheese and butter pieces, then pulse until the mixture resembles coarse crumbs.
Transfer the mixture to a large bowl. Pour in the buttermilk and gently stir just until the dough comes together. The dough may look slightly dry, but avoid overmixing.
Turn the dough out onto a lightly floured surface and knead gently 3 to 4 times, just until smooth. Pat or roll the dough into a rectangle about ¾-inch thick, roughly 8 x 6 inches.
Cut the dough into twelve 2-inch squares and place them on the prepared baking sheet.
Bake for 12 to 15 minutes, or until the biscuits are golden brown and baked through. Transfer to a wire rack and allow to cool for about 5
Enjoy!