With a mixer, cream butter on medium-high speed until soft and smooth.
Add both sugars to the creamed butter and mix until fully incorporated. With the mixer on medium-high speed, add the egg to the mixture and beat until the batter looks uniform.
In a separate bowl, combine the flour, cornstarch, baking soda, salt and nutmeg. Gently fold into the batter until just combined. Fold in shredded apples.
Prepare a greased or parchment lined cookie sheet. Form balls of dough and roll them around in the cinnamon sugar mixture. Place the dough balls on the sheet, about 3 inches apart. Use your fingers to press and flatten the dough slightly.
Bake for 8-10 minutes, or until the cookies are light golden brown. They should be soft and chewy. Remove cookies from sheet and cool on a wire rack.
For this recipe and more, visit www.thecomfortofcooking.com