For the Shortbread Cookies

1. Preheat your oven to 350 degrees Fahrenheit. Line metal baking sheets with parchment paper to ensure the cookies come off of the pan cleanly after baking.
2. In a large bowl with a hand mixer or in the bowl of a stand mixer fitted with a paddle attachment, beat the cold butter and granulated sugar together on high speed until smooth. This should be about 3 minutes of mixing until light and fluffy.
3. Add vanilla extract to the batter and beat until smooth.
4. Slowly, beat the all purpose flour and salt into the dough. Only mix until you see the flour disappear into the batter.
5. Divide the dough into 1-tablespoon balls. Use your thumb or pinky finger to create a deep indent in the center of each cookie.
6. Place the cookies about 1.5-2 inches apart on your prepared baking sheets. Bake for 8-11 minutes or until the edges start to turn light golden brown in color and the tops look pale and slightly shiny.
7. Use your thumb or the back of a spoon to push into the center of the cookies and deepen the indents. This will allow you to add more peach filling to each cookie.
8. Allow the cookies to cool before filling.

For the Peach Pie Filling

1. Prepare the peach filling by adding granulated sugar, light brown sugar, corn starch, and cinnamon to a medium sized saucepan over medium heat. Stir until the mixture turns thick and begins to bubble, about 2-3 minutes.
2. Pour the chopped peaches into the mixture and stir until the mixture begins to thicken and the peaches have softened. This should take anywhere between 3-5 minutes or until the filling is firmer rather than liquidy.
3. Remove the filling from the heat and allow it to cool before using. The peach filling can be made ahead of time and stored in the fridge for up to 3 days or in the freezer for up to 3 months.

For the Glaze

1. In a medium bowl, use a spoon to mix the powdered sugar and milk together until smooth. The glaze should look thick. If the icing looks runny or watery at all, add powdered sugar by the tablespoon until the glaze is thick. If the icing is too thick to stir, add milk by the teaspoon.
2. If desired, transfer the glaze to a piping bag or a zippable plastic bag with the corner snipped off of it for more control.

For Decorating

1. Add about 1 tablespoon of peach pie filling to the center of each cookie.
2. Drizzle the glaze over the top of each cookie as desired.
3. Store the cookies in an airtight container or tightly covered in the fridge for up to 5 days or in the freezer for up to 2 months.