For the cookies: Sift the flour, graham cracker crumbs, baking soda, baking powder and salt into a large bowl.
Beat the granulated sugar and butter together in another large bowl with an electric mixer on medium-high speed until light and fluffy, about 5 minutes. Add the egg and beat until incorporated, then beat in the vanilla. Alternate adding the dry ingredients and the milk, beginning and ending with the dry ingredients. Mix until just incorporated. Cover and refrigerate the dough until chilled, about 1 hour.
Position the oven racks in the top and bottom thirds of the oven and preheat to 400 degrees F. Line 2 baking sheets with parchment paper and lightly coat with cooking spray.
Drop tablespoonfuls of batter about 3 inches apart on the prepared baking sheets (about 6 cookies per baking sheet). (Keep the remaining batter chilled while working.)
Bake until the cookies puff up and the tops are no longer glossy, about 7 minutes. Let cool for a few minutes on the baking sheets, then transfer to a wire rack to cool completely, about 1 hour. Let the baking sheets cool, then reline with fresh parchment, lightly coat with cooking spray and bake the remaining batter.
For the filling: Beat the confectioners' sugar, butter and cream cheese in a large bowl with an electric mixer on medium speed until fluffy. Add the marshmallow creme, milk, lime zest and juice and beat until light and airy, about 5 minutes.
Spread a heaping tablespoon of the filling on half of the cookies. Sandwich with the remaining halves, pushing down slightly to move the filling to the edge.
This recipe has been updated and may differ from what was originally published or broadcast.