01 - Whisk together sweetened condensed milk, Greek yogurt, key lime juice, lime zest, vanilla, and a pinch of salt in a large bowl until fully combined.
02 - In a separate chilled bowl, whip the heavy cream to stiff peaks. Gently fold the whipped cream into the lime mixture until the texture is smooth and even.
03 - Line a 9x9-inch pan with parchment paper, pour in the prepared ice cream mixture, smooth the top, and freeze for at least 4 hours or until set.
04 - Preheat the oven to 350°F. Line a baking sheet with parchment paper.
05 - Combine graham cracker crumbs, flour, baking powder, and salt in a bowl and whisk to blend.
06 - In a separate bowl, beat unsalted butter with packed brown sugar until light and fluffy. Beat in the egg and vanilla extract until thoroughly incorporated.
07 - Gradually stir the dry ingredient mixture into the wet mixture just until no dry streaks remain.
08 - Scoop 16 tablespoon-sized balls of dough onto the prepared baking sheet and gently flatten. Bake for 8 to 10 minutes or until cookies are golden. Allow cookies to fully cool on a rack.
09 - Remove the ice cream from the freezer. Using a round cookie cutter matching the cookie size, cut out ice cream discs. Place each disc between two graham cracker cookies to assemble the sandwiches.
10 - Serve the sandwiches immediately or individually wrap and return to the freezer until ready to serve.