Whisk flour, baking powder, baking soda, cinnamon, and nutmeg together in a small bowl.
Combine marmalade, eggs, oil, brown sugar, and vanilla extract in a large bowl, and mix until combined.
Stir in walnuts and carrots, and then stir in the dry ingredients, until just combined.
Pour ⅔ cup of carrot cake batter into the bottom of the springform pan. Even it out, to cover the whole bottom. Drop large spoonful's of cheesecake and carrot cake batter alternatively into the springform pan, until both batters have been used up. Do not mix or swirl them together.
Cover the outside of springform pan with aluminum foil. Place the springform pan in a crock pot liner bag. A chicken bag works well too. You want the bag to go up the whole sides of the pan. Tie or use a wire tie to tighten the bag around the pan.
Place the springform pan in a larger pan, and fill the larger pan with water to go halfway up the sides of the springform pan. Bake for 1 hour 30 minutes, or until the center of the cheesecake is slightly jiggly.
Turn off the oven and leave the cheesecake inside for 30 minutes. Crack open the oven door and leave the cheesecake in for another 30 minutes. Remove from oven and leave the cheesecake to cool at room temperature for about an hour. Remove from water bath, cover, and cool in the refrigerator for at least 6 hours.