Preheat your oven to 450°F. In a food processor, pulse the flours, sugar, baking powder, salt, and soda. Add the frozen cream cheese and butter. Pulse only until the mixture looks like "coarse gravel"—you want visible chunks of fat left.
Transfer to a bowl and stir in the cold buttermilk. The dough should be shaggy and look slightly dry; do not over-mix here or the biscuits will become tough.
Turn the dough onto a floured surface. Instead of just kneading, pat it into a rectangle. Fold it in half. Turn it 90 degrees and pat it down again. Repeat this "fold and pat" 5 or 6 times.
This creates physical layers of flour and cold fat that will puff up in the oven.
Press the dough into a 3/4-inch thick rectangle. Use a very sharp knife or biscuit cutter to cut into 12 squares. Crucial: Do not "twist" the cutter; press straight down and pull straight up. Twisting seals the edges and prevents the biscuit from rising.
Place the biscuits on a parchment-lined sheet so they are just touching. This helps them climb upward rather than spreading outward.
Bake for 12–15 minutes until the tops are golden brown.
Brush the hot tops with melted butter and a tiny sprinkle of flaky salt for a professional savory-sweet contrast.