In a separate bowl, add the butter, white sugar, brown sugar, and vanilla. Beat with a hand mixer for 1-2 minutes, or until fluffy. Add the eggs one at a time, beating until well incorporated. Add the carrots and mix again.
Add the dry ingredients and mix on low just until no dry streaks remain.
Form 12 cookie dough balls, about 55g each, and place them on a plate. Freeze for 30–60 minutes, until firm but still pliable. Alternatively, cover the dough with plastic wrap and refrigerate for up to 4 days.
Preheat the oven to 180C (355F) and line two baking sheets with parchment paper.
Take one cookie dough ball from the freezer at a time and roll it between two pieces of plastic wrap into a disk using a rolling pin. Remove one frozen filling portion from the freezer and place it in the center of the dough disk.
Enclose the cheesecake filling by wrapping the dough around it, then roll the filled dough between your palms to form a smooth ball. Place it in the fridge while you assemble the remaining cookies.
Arrange the filled cookie dough balls on the baking sheets, leaving space between each one.
Bake one batch at a time, keeping the second batch in the fridge while the first bakes, for 15-17 minutes, or until the cookies have spread, puffed up, and turned golden around the edges.
Remove from the oven and let the cookies cool on the baking sheets for 10 minutes before transferring them to a wire rack to cool completely.