01 - In a large bowl, whisk together the sweetened condensed milk, Greek yogurt, key lime juice, key lime zest, vanilla extract, and salt until fully incorporated.
02 - Using a chilled bowl, whip the heavy cream with an electric mixer until stiff peaks form.
03 - Gently fold the whipped heavy cream into the lime mixture until smooth and no streaks remain.
04 - Line a 9x9-inch pan with parchment paper. Pour in the ice cream base and smooth the surface. Freeze for at least 4 hours or until completely firm.
05 - Preheat oven to 350°F. Line a baking sheet with parchment paper.
06 - In a bowl, combine graham cracker crumbs, all-purpose flour, baking powder, and salt.
07 - In a separate mixing bowl, beat the unsalted butter and brown sugar until light and fluffy with an electric mixer. Add the egg and vanilla extract; mix well.
08 - Gradually add the dry ingredients to the butter mixture, stirring just until a dough forms. Do not overmix.
09 - Portion 16 tablespoon-sized balls of dough onto the prepared baking sheet. Flatten each slightly. Bake for 8 to 10 minutes until golden. Cool completely on a rack.
10 - Once the ice cream is set, use a round cookie cutter to cut out ice cream discs matching cookie size. Sandwich each disc between two graham cracker cookies.
11 - Enjoy immediately or wrap sandwiches individually and freeze until ready to serve.