How to Make It
Preheat oven to 350°F. Mix together flour, baking powder, baking soda, salt, and spices in a large mixing bowl. In a separate bowl, whisk together oil, sugar, eggs, and ginger until well combined. Add to the dry ingredients and mix with a spoon until completely homogenous. Fold in shredded carrot and pecans. Pour mixture into a greased 9-inch springform cake pan and bake until a toothpick inserted into the center comes out clean, 23 to 25 minutes. If the cake has domed in the middle, press the cake down to create a perfectly even surface. Set aside to cool.
Preheat oven to 350°F. Beat together cream cheese, sour cream, brown sugar, and granulated sugar until smooth and fluffy, about 5 minutes. Use a spatula to scrape the sides and bottom of the bowl. Add eggs one at a time, waiting until each egg is fully incorporated before adding another. Scrape the bowl again, add the remaining ingredients, and beat for an additional 2 minutes.
Pour Cheesecake mixture over Carrot Cake and spread evenly throughout the pan. Wrap the bottom and sides of the springform pan in several layers of aluminum foil. Place the cake pan in a large roasting pan and fill the roasting pan with water so that it comes a little over halfway up the side of the cake pan. Bake for 1 hour. Turn off the oven and allow the cheesecake to stay in the oven for an additional 30 minutes. Remove cheesecake from oven, remove pan from water bath, and gently run a knife around the edge of the cheesecake. Refrigerate cheesecake for 8 hours or overnight before removing from springform pan.