01 - Combine sweetened condensed milk, Greek yogurt, key lime juice, lime zest, vanilla extract, and salt in a large bowl. Whisk vigorously until the mixture is smooth.
02 - In a separate chilled bowl, whip the heavy cream with an electric mixer or whisk until stiff peaks form. Using a spatula, gently fold the whipped cream into the lime mixture until fully blended and smooth.
03 - Line a 9x9-inch pan with parchment paper. Pour the ice cream mixture into the pan, smoothing the top evenly. Freeze for at least 4 hours, or until completely 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. Stir until well mixed.
06 - In a separate large bowl, beat unsalted butter and brown sugar until the mixture is light and fluffy. Add egg and vanilla extract; beat until just combined.
07 - Gradually add the dry mix to the creamed mixture, stirring just until the dough forms. Avoid overmixing.
08 - Scoop 16 tablespoon-sized balls of dough onto the prepared baking sheet. Flatten each ball slightly with your hand. Bake for 8 to 10 minutes, or until golden brown. Allow to cool completely on a wire rack.
09 - Once ice cream is firm, remove from the pan and cut out 8 discs using a round cookie cutter matching the cookie size.
10 - Sandwich each ice cream disc between two graham cracker cookies. Serve immediately, or wrap sandwiches individually and freeze until serving time.