Sift all-purpose flour, cake flour, baking powder, baking soda, and granulated sugar into the bowl of a stand mixer (or use a large bowl if using a hand mixer). Mix with a paddle attachment on the lowest speed until combined.
Stop the mixer and add the butter. Begin to mix the butter into the flour on the lowest speed until it just begins to incorporate. Increase the speed to low and continue to mix for approximately 3 minutes (or until the butter is broken up and incorporated into the dry mixture). If there are any large butter pieces that haven’t incorporated, stop the mixer and break them up with your fingertips.
Next, turn the mixer to slow and gradually pour in the cream. Add the sour cream and mix for 30 seconds until the dry ingredients are moistened and the dough begins to come together. Scrape the sides and bottom of the bowl as necessary.
Cut the frozen cinnamon butter paste into ¼-inch cubes and fold them into the mixed dough. Don’t worry if they start to break up a little. That will be fine.
Mound the dough on a large sheet of plastic wrap and use your hands to press the dough into a 7½-by-10-inch block. Straighten the edges as best as you can. This method will make rectangular scones. If you want triangular scones, divide the dough in half and press each half into circles. Cover the shaped dough in plastic wrap and refrigerate for 2 hours, or until firm.