Begin by finely grinding graham crackers in a food processor until they resemble crumbs. In a mixing bowl, combine these crumbs with all-purpose flour and brown sugar thoroughly. Next, add softened unsalted butter to the dry ingredients, mixing until a soft, cohesive dough forms.

Preheat your refrigerator and line a baking sheet with parchment paper. Using your hands, take a portion of the dough, roll it into balls about the size of a tablespoon, and arrange them neatly on the lined baking sheet. Press your thumb into the center of each ball to create an indentation. Place the cookies in the freezer for at least 30 minutes.

While the dough chills, zest and juice your fresh Key limes. In a medium bowl, whisk together the lime juice, zest, and egg yolk. Gradually add sugar while mixing until the filling is smooth and well combined.

Preheat your oven to 350°F (175°C). Once your cookies are chilled, bake for 10-12 minutes, or until the edges are lightly golden. Press your thumbprint deeper into each cookie while they’re still warm.

Spoon the prepared lime filling into each thumbprint, filling them generously. Return to the oven and bake for an additional 5-7 minutes, or until the filling has set.

Remove the cookies from the oven and transfer them to a wire rack. Allow to cool completely before dusting with powdered sugar.