Prepare the key lime cheesecake filling at least an hour in advance. In a bowl, combine cream cheese, icing sugar, key lime zest, and key lime juice.
Line a plate or small baking sheet with parchment paper. Scoop out 23 heaping teaspoons of the cheesecake mixture onto the parchment paper. Freeze for 45 minutes or until firm. Note: If using vegan cream cheese, freezing time may be longer.
In a large bowl, use a handheld mixer to cream together butter, white sugar, light brown sugar, and key lime zest until fluffy. Add the egg, vanilla extract, and key lime juice. Beat until well combined.
Gradually add the flour, baking soda, and salt to the wet mixture. Mix until just combined.
Preheat the oven to 350°Fahrenheit. Line two baking sheets with parchment paper.
Scoop out the cookie dough into 2 tablespoon-sized balls and place them on the prepared baking sheets.
Remove the key lime cheesecake filling from the freezer. Press one into the center of each cookie dough ball, gently pressing down.
Use your hands to cover the cream cheese filling with the dough, ensuring it's completely encased.
Bake the cookies one sheet at a time for 9-12 minutes, or until the edges are set and they're a light golden brown. While one baking sheet is in the oven, keep the other in the fridge to prevent the dough from becoming too warm.