Step 1: Prepare the Pickle-Brined Carrots and Pecans (Optional, but Recommended). In a small bowl, combine 1/4 cup dill pickle brine and 1/4 cup water. Add the reserved 1/2 cup grated carrots. In another small bowl, combine the other 1/4 cup dill pickle brine and water, add the pecans. Let both sit at room temperature.

Step 2: Make the Cake Batter. Preheat the oven to 350°F (175°C). In a large bowl, whisk together the sugar, oil, and eggs.

Step 3: Combine Dry Ingredients. In a separate bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt.

Step 4: Combine Wet and Dry Ingredients. Add the flour mixture to the egg mixture and whisk to combine.

Step 5: Add Carrots and Pecans. Drain the brined carrots very well. Stir in all the carrots (brined and regular) and 1/2 cup of the drained pecans, mixing well.

Step 6: Prepare Springform Pan. Lightly grease a 9-inch springform pan with nonstick cooking spray.

Step 7: Bake the Cake Layer. Pour the carrot cake batter into the pan and spread into an even layer. Bake until the edges of the cake are just set and the top is no longer shiny, about 18 minutes.

Step 8: Cool Cake Layer. Let cool for 30 minutes.

Step 9: Make the Cheesecake Batter. Meanwhile, reduce the oven temperature to 325°F (160°C). In the bowl of a stand mixer fitted with a paddle attachment, beat the cream cheese on medium speed until no lumps remain, about 2 minutes.

Step 10: Add Remaining Cheesecake Ingredients. Gradually add the sour cream, sugar, flour, salt, and dill pickle powder, beating on medium speed until the batter is smooth and creamy, about 1 minute. Scrape down the sides and bottom of the bowl as needed.

Step 11: Add Eggs and Vanilla. Reduce the mixer to medium-low speed and add the eggs, one at a time, beating until just combined after each addition. Continue scraping down the sides and bottom of the bowl as needed. Stir in the vanilla. Set aside.

Step 12: Pour Cheesecake Batter over Cake Layer. Starting at the outer edges, carefully and evenly pour the cheesecake batter over the cooled carrot cake layer, finishing in the center.

Step 13: Bake. Place the pan on a rimmed baking sheet and bake until the edges of the cheesecake are set and the center just barely jiggles when the pan is shaken, 50 to 55 minutes.

Step 14: Cool Completely. Transfer the pan to a wire rack to cool completely, about 2 hours.

Step 15: Chill. Cover and chill for at least 8 hours.

Step 16: Serve. To serve, run a knife along the sides of the pan to loosen. Remove the sides of the springform pan. Decorate the top of the cheesecake with the remaining pecans. Slice and serve. Garnish with fresh dill (optional).