Step 1

For the carrot cake: Adjust an oven rack to the middle position and preheat to 350 degrees F. Spread 1/2 cup of the pecans on a rimmed baking sheet and bake until golden and toasted, 10 to 12 minutes. Allow to cool, and then finely chop.

Step 2

Combine the pecans, flour, baking powder, baking soda, cinnamon, ginger and 1/4 teaspoon salt in a large bowl. Whisk together the oil, sugar and eggs in a separate bowl. Stir the carrots into the egg mixture. Fold the carrot-egg mixture into the flour mixture until just combined. Pour into an ungreased 9-inch springform cake pan and tap it on the counter to even out the batter. Bake until the cake bounces back when pressed and a toothpick inserted in the middle comes out clean, 20 to 25 minutes. Cool completely. The cake can be made a day ahead and stored in the pan.

Step 3

For the cheesecake: Preheat the oven to 350 degrees F. Beat the cream cheese, sour cream and granulated sugar in a stand mixer fitted with a paddle attachment until smooth and creamy, about 5 minutes, scraping down the sides of the bowl as needed. Add the eggs one at a time, beating well after each addition. Beat in the flour, lemon zest and juice and vanilla, about 1 minute.

Step 4

Pour the cheesecake mixture over the carrot cake. Wrap the bottom and sides of the pan with a large piece of foil. Put in a roasting pan or a large baking dish and fill halfway up the sides of the cake pan with water. Bake until the cheesecake is pale yellow and just jiggles slightly in the center, about 1 hour. Turn off the oven and let the cheesecake rest in the hot oven for 30 minutes. Remove, run a sharp knife around the edge and let cool completely on a rack. Cover and refrigerate 8 hours or overnight.

Step 5

For the sour cream topping: Whisk together the confectioners' sugar, sour cream, vanilla and salt. Spread on top of the cheesecake; garnish with chopped pecans. Refrigerate for at least 30 minutes before serving. Cut into slices and serve.