01 - Whisk together sweetened condensed milk, Greek yogurt, key lime juice, key lime zest, vanilla extract, and salt in a large mixing bowl until fully blended.
02 - In a separate chilled bowl, whip heavy cream with an electric mixer until stiff peaks form. Gently fold the whipped cream into the lime mixture, creating a smooth, homogeneous base.
03 - Line a 9x9-inch square pan with parchment paper. Evenly spread the ice cream mixture into the pan, smoothing the top. Freeze for at least 4 hours or until firm.
04 - Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
05 - Combine graham cracker crumbs, all-purpose flour, baking powder, and salt in one bowl and set aside.
06 - In a separate large bowl, beat unsalted butter and brown sugar until light and fluffy. Mix in the egg and vanilla extract, blending until incorporated.
07 - Gradually add the dry ingredients to the butter mixture, stirring just until no dry spots remain and a cohesive dough forms.
08 - Scoop 16 tablespoon-sized portions of dough onto the prepared baking sheet, spacing evenly. Flatten each slightly and bake for 8 to 10 minutes until golden brown. Allow cookies to cool completely.
09 - Remove the frozen ice cream slab from the pan using the parchment. Cut out 8 discs with a round cookie cutter matching the cookie size.
10 - Place a disc of ice cream between two graham cracker cookies to form a sandwich. Enjoy immediately or wrap individually and freeze until ready to serve.