Position rack in the center of the oven. Preheat oven to 400 Fahrenheit. Lightly coat a large baking sheet with cooking spray.

Combine the flours, baking soda, and baking powder into the bowl of an electric mixer. Fit the mixer with the paddle, not the wire whisk. Use the lowest speed to mix in the salt, 1 cup sugar, and cornmeal. Mix briefly until the dry ingredients look evenly distributed. Add the pieces of butter and mix on low for several seconds until the butter pieces are about the size of corn kernels.

Make a well in the center of the dry ingredients and pour in the egg, buttermilk, and dried cherries. Mix on low for about 15 seconds until the dry ingredients are moist and there is still a little flour on the bottom of the bowl. Let stand 5 minutes.

Use a small ice cream scooper or a soup spoon to scoop scant spoonfuls of batter onto the cookie sheet. Use your hand to lightly flatten the scoops and mold round or oval shapes. Place the scoops about half an inch apart on the sheet. You should have enough for 20 scones. Sprinkle tops of scones with remaining tablespoon of sugar. Bake for 20 to 25 minutes until tops are golden brown. Allow to cool on a wire rack for 10 minutes and eat as soon as possible. Store overnight in an airtight container, if necessary.