Adjust oven rack to the middle position and heat oven to 450. Line a baking sheet with parchment paper and set aside.
Pulse the flour, sugar, baking powder, salt and baking soda together in a food processor to combine. scatter the butter and cream cheese over the top and continue to pulze until the mixture resembles coarse meal, about 15 pulses. Transfer the mixture to a large bowl. Stir in the buttermilk with a spatula until the dough comes together.
Turn out the dough onto a lightly floured counter. Knead the dough gently until smooth, 8 10 times. Pat the dough into a 9: circle, about 3/4" thick.
Using a floured cutter, stamp out 6 biscuits and arrange upside down on the prepared baking sheet. Gather the remaining dough, pat into a 3/4" thick circle and stamp out the remaining 6 biscuits.
Bake until the biscuits begin to rise, about 5 minutes, then rotate the baking sheet and reduce the oven temperature to 400 degrees. Continue to bake until golden brown, 12 to 15 minutes longer. Transfer the biscuits to a wire rack and let cool for 10 minutes before serving.
Note: The biscuits can be stored in an airtight container at room temperature for up to 3 days.