01 - Whisk sweetened condensed milk, Greek yogurt, key lime juice, lime zest, vanilla extract, and a pinch of salt in a large mixing bowl until smooth.
02 - In a separate chilled bowl, beat heavy cream with an electric mixer until stiff peaks form. Carefully fold the whipped cream into the lime mixture until uniform and smooth.
03 - Line a 9x9-inch pan with parchment paper. Transfer the ice cream mixture into the pan, smoothing the top. Freeze for a minimum of 4 hours, until firm.
04 - Preheat oven to 350°F. Line a baking sheet with parchment paper.
05 - In a medium bowl, combine graham cracker crumbs, all-purpose flour, baking powder, and salt.
06 - In another bowl, beat unsalted butter and packed brown sugar until light and fluffy. Add egg and vanilla extract, mixing well.
07 - Gradually add flour mixture to the creamed butter, stirring until just combined; avoid over-mixing.
08 - Portion out 16 tablespoon-sized balls of dough onto the prepared baking sheet. Flatten slightly. Bake for 8-10 minutes until golden. Cool completely on a rack.
09 - Once the ice cream base is frozen, use a round cookie cutter matching the cookie size to cut out 8 ice cream rounds.
10 - Place one ice cream disc between two graham cookies. Serve at once, or wrap sandwiches individually and store in the freezer until serving.