01 - In a large mixing bowl, whisk together sweetened condensed milk, Greek yogurt, fresh key lime juice, lime zest, vanilla extract, and a pinch of salt until smooth.
02 - In a separate chilled bowl, whip heavy cream to stiff peaks using an electric mixer on medium-high. Gently fold the whipped cream into the lime mixture until fully blended and silky.
03 - Line a 9x9-inch pan with parchment paper. Transfer ice cream mixture into the pan and spread evenly. Freeze for at least 4 hours or until firm.
04 - Set oven to 350°F. Line a baking sheet with parchment paper for the cookies.
05 - In a medium bowl, combine graham cracker crumbs, all-purpose flour, baking powder, and salt.
06 - In a separate bowl, beat unsalted butter and brown sugar until light and fluffy. Add egg and vanilla extract, mixing well.
07 - Gradually incorporate dry ingredients into the butter mixture, stirring just until combined. Do not overmix.
08 - Scoop 16 tablespoon-sized balls of dough onto the prepared baking sheet, flattening them slightly. Bake for 8 to 10 minutes until golden. Allow cookies to cool completely.
09 - Using a round cookie cutter equal to the cookie size, cut out discs of frozen ice cream. Sandwich each disc between two graham cracker cookies.
10 - Serve immediately or wrap sandwiches individually and return to the freezer until serving time.