Add the butter, granulated sugar, and brown sugar to the bowl of a stand mixer. Mix on medium speed for 5 minutes. It should be light and fluffy. Add in the egg and vanilla extract and mix until combined.
In a separate bowl, mix together the dry ingredients. Transfer the dry ingredients to the stand mixer and mix until combined.
Place the shredded apples into a tea towel or cheesecloth and squeeze out as much moisture as possible. Add to the stand mixer and mix to combine.
Refrigerate for at least 30 minutes before baking.
Preheat oven to 350℉.
Using a 1.5-tablespoon scoop, scoop the cookie dough and place it on the cookie sheet. Press a caramel into the center of the cookie dough.
Bake for 11 minutes. Allow to cool completely before frosting the cookies.
To make the frosting add the cream cheese, butter, powdered sugar, and vanilla extract to a large bowl. Using a hand mixer, mix until well combined.
Spread 1.5 tablespoons of the frosting on the cooled cookies. Garnish with apple pieces and drizzle with caramel sauce.