Preheat the oven to 350 °F (175 °C). Lightly grease a 10-inch springform pan.
In a medium bowl, beat the cream cheese and granulated sugar until smooth. Add the eggs, one at a time, then stir in flour, vanilla and sour cream. Set aside.
In a large bowl, combine vegetable oil, brown sugar and granulated sugar. Add eggs and vanilla and beat until light and creamy. Stir in flour, baking soda, cinnamon, nutmeg and salt, then mix in the grated carrots.
Spread half of the carrot cake batter into the prepared pan. Dollop half of the cheesecake batter over the carrot cake (do not swirl). Then spoon the remaining carrot cake batter on top. Finally spread the remaining cheesecake batter over the top.
Bake for about 60-70 minutes or until the edges are set and the center still has a slight jiggle. Tent with foil if browning too quickly.
Allow the cake to cool completely in the pan on a wire rack. Then chill in the refrigerator for at least 2-3 hours (or overnight) until fully set.
To make the frosting, beat together the cream cheese and butter until smooth. Gradually add powdered sugar, then vanilla and sour cream until well combined. Spread over the chilled cake and sprinkle with chopped pecans around the edge.
Slice and serve chilled.
Notes
You can make the cake a day ahead and keep it refrigerated. If desired, substitute toasted walnuts for the pecans garnish.