Prepare a muffin tin by lining it with cupcake liners. Preheat the oven to 350 degrees.
Combine the flour, baking powder, baking soda, cinnamon, nutmeg and salt in a medium bowl.
Whisk together in a separate medium bowl the white and brown sugar, eggs and oil until well combined. Stir in the shredded carrots.
Stir the dry ingredients into the wet ingredients until just combined.
Scoop about 1 ½ tablespoon of carrot cake batter into each cupcake liner. Top with about 1-2 tablespoon of cheesecake filling, smoothing out the filling with a knife or spoon to cover the carrot cake batter.
Bake for about 22-24 minutes or until mostly set in the middle. Cool in the pan for 15 minutes and then transfer to the refrigerator while still in the muffin tin to chill for 1-2 hours. Once completely cooled, frost the top of the cupcakes with a dollop of cream cheese frosting. See notes above about storing and freezing.