In a stand mixer fitted with the paddle attachment, beat together the butter, granulated sugar, and brown sugar on medium-high speed until light and fluffy, about 2 minutes.
Use a silicone spatula to scrape down the sides and bottom of the bowl, then add the egg, vanilla, lime juice, and lime zest. Beat on medium-high until smooth and fluffy, about 1 minute.
Add the flour, baking powder, baking soda, and salt and beat on low speed until just combined and no streaks of flour remain, about 30 seconds, scraping down the bowl as needed. Last, add the graham cracker crumbs and mix until combined.
Use a 1 ½ ounce cookie scoop to portion out equal amounts of dough. Roll the dough in your hands to smooth the edges, then place on the prepared baking sheets, spacing the dough balls about 2 inches apart. Use your thumb or the back of a tablespoon to make an indentation in the center of each cookie, shaping it gently so the edges are smooth and there is a wide divot in the middle.
Bake the cookies for 12 to 14 minutes or until they’ve puffed up and are set and firm around the edges, but still soft in the middle. Remove the baking sheet from the oven and take the bake of a measuring cup reshape the divot in the hot cookies, making it wide and shallow with about 1/4 inch border all around the edge. Set aside to cool until set, about 5 minutes, before transferring to a cooling rack to cool completely.
Once the cookies are cool, make the key lime pie filling. In the bowl of a stand mixer fit with the paddle attachment, combine all of the ingredients for the filling and beat until smooth and no chunks of cream cheese remain, about 1 minute.
Spoon about 2 teaspoons of the key lime filling into the center of each cookie, using the back of a spoon to spread it into an even layer. You can also put the filling into a piping bag and pipe it in! Top with fresh lime zest and a key lime slice if desired. Refrigerate for at least 1 hour for the filling to set before serving!