Preheat oven to 350 degrees. Combine first four dry ingredients in bowl and set aside.
In mixing bowl beat sugar, butter, and apple sauce until smooth. Add the egg and beat until the batter is light and fluffy.
Mix in the buttermilk and 1 Tbsp. zest, followed by the dry ingredients.
Place dough in rounded teaspoons on cookie sheet and bake for 10 minutes. Do not brown the cookies.
In a small bowl with fork mix powdered sugar, 1 Tbsp. zest, and juice to frost the cookies. Place in refrigerator while waiting for cookies to cool.
Frost cooled cookies.