Preheat the oven to 350°F. Line a baking sheet with parchment paper or a baking mat, set aside.
In the bowl of a stand mixer cream the butter, brown sugar, and granulated sugar, about 2-3 minutes.
Add the eggs, vanilla extract, and light corn syrup and mix to combine.
Add the flour, graham cracker crumbs, cornstarch, baking soda, baking powder, and salt and mix until combined.
Use a ¼ cup to portion the dough into round balls. Place 6 balls of dough on a baking sheet.
Bake for 11-13 minutes or until edges are slightly golden and tops are just set.
Spray the bottom of a glass cup with nonstick cooking spray. You want the cup to be smaller than the cookie. Remove the cookies from the oven and immediately use the bottom of the glass cup to press down in the center of each cookie to create an indentation. (This is where the lime filling will be placed once the cookies are cool).
Let cookies stay on baking sheet for 10 minutes before transferring to a wire rack to cool completely. While the cookies are cooling make the lime filling.