Preheat the oven to 350°F and line a 9 x 9 square pan with parchment paper on all sides. Combine the brown sugar and butter together in a mixing bowl. Whisk to combine. Add the vanilla extract, eggs and carrots and mix.
Add the flour, cinnamon, baking powder, salt, and orange zest and mix until only just combined and no streaks of flour remain. Do not overmix!
Pour the carrot cake batter into your prepared pan and set aside while you make the cheesecake layer.
Combine the softened cream cheese, egg, granulated sugar and vanilla together in a mixing bowl and beat together (if using a stand mixer, use the paddle attachment) until creamy and homogenous. Don’t over mix as this will beat too much air into your batter.
Drop dollops of the cheesecake batter on top of the carrot cake batter and use a butter knife to make big swirls. Bake the bars at 350°F for 30 minutes or until a knife inserted into the middle comes out mostly clean.
Allow the bars to cool completely to set up before slicing into squares and enjoying!