Preheat your oven to 350°F (175°C). Line the bottom of a 9-inch springform pan with parchment paper and grease the sides.

In a large mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.

In another bowl, blend the granulated sugar, brown sugar, and vegetable oil until well combined. Add the eggs one at a time, mixing well after each addition.

Gradually add the dry ingredients to the wet mixture and stir until just combined. Fold in the grated carrots and chopped pecans.

Pour the carrot cake batter into the prepared springform pan and bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Let it cool completely.

In a mixing bowl, beat the softened cream cheese until smooth. Gradually add the 1/2 cup granulated sugar and vanilla extract, mixing until creamy.

Add the eggs one at a time, mixing just until blended. Stir in the sour cream until everything is smooth.

Carefully pour the cheesecake batter over the cooled carrot cake layer. Bake in the preheated oven for 55-60 minutes until the edges are set and the center still has a slight jiggle.

Once done, turn off the oven and crack the door open. Let the cheesecake cool inside for about an hour.

Transfer to the refrigerator to chill for at least 4 hours (preferably overnight).