For a more savory version of these layered biscuits, leave out the cinnamon and sugar.
Preheat oven to 500 degrees. In a small bowl, combine the cinnamon and sugar, and stir until well mixed; set aside. In a medium bowl, whisk together the flour, salt, baking powder, and baking soda. Add butter, and use a pastry blender or two knives to cut the butter into the flour mixture until it is the size of peas. Add buttermilk, and mix with a spoon just until it forms a sticky dough.
Transfer to a lightly floured work surface, and bring dough together. Roll dough into an 8-by-11-by-3/4-inch rectangle, and sprinkle 1/2 tablespoon cinnamon sugar in the center section of the rectangle. Use a bench scraper or a spatula to lift the ends, folding the rectangle like a letter into thirds toward the center. Before folding the second end over, sprinkle another 1/2 tablespoon cinnamon sugar onto the opposite flap. Fold the second flap over. Give the dough a quarter turn, and repeat the rolling, sprinkling, and folding. Transfer dough to a parchment-lined baking sheet, wrap it in plastic wrap, and chill in the refrigerator for 20 minutes.
Remove from refrigerator, and return to work surface. Roll to a 1/2-inch-thick rectangle, and repeat sprinkling and folding method as in step 2 (when rolling out the second time, do not fold). Cut out with a 2 1/4-inch round biscuit or cookie cutter, and transfer to a baking sheet.
Sprinkle tops with remaining cinnamon sugar, and place in 500 degree oven for 4 minutes. Reduce heat to 375 degrees. Continue baking until biscuits begin to brown all over, 20 to 25 minutes. Remove from oven; cool on a wire rack. Serve warm.