Mix cinnamon sugar on a plate; set aside. Mix flour, baking powder, baking soda, cinnamon and salt in a medium bowl. Whisk sugar and butter in a large bowl. Whisk in egg and then buttermilk until smooth. Gently stir in dry ingredients with a spatula to form soft, pliable dough. Cover with plastic and refrigerate for at least 30 minutes and up to overnight. When ready to fry, heat 1 inch of oil in a 10-inch heavy skillet to 325 degrees. Meanwhile, use a rounded teaspoon measure to scoop all of the dough into balls. Working in batches, drop dough balls into hot oil. fry until golden brown on one side, 1 to 2 minutes. flip and continue to fry until golden on remaining side, another 1 to 2 minutes. Drain all doughnut holes on a brown paper bag, and quickly dredge in cinnamon surgar, serving warm or at room temperature.