1. Prepare the Carrot Cake Layer

1. Preheat Oven: Preheat your oven to 350°F (175°C). Grease and line a 9-inch springform pan with parchment paper.
2. Mix the Dry Ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, ginger, cloves, and salt. Set aside.
3. Combine the Wet Ingredients: In a large mixing bowl, whisk together the vegetable oil, granulated sugar, brown sugar, eggs, and vanilla until well combined.
4. Add Carrots and Mix-Ins: Stir in the grated carrots, drained pineapple, and optional nuts and raisins.
5. Combine Wet and Dry Ingredients: Gradually add the dry ingredients to the wet mixture, stirring until just combined. Do not overmix.
6. Bake the Carrot Cake Layer: Pour the batter into the prepared springform pan and bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Let cool slightly, then transfer to a wire rack to cool completely.

2. Prepare the Cheesecake Layer

1. Reduce Oven Temperature: Lower the oven temperature to 325°F (163°C).
2. Mix the Cream Cheese: In a large mixing bowl, beat the cream cheese with a hand or stand mixer on medium speed until smooth and creamy, about 2 minutes.
3. Add Sugar and Eggs: Add the granulated sugar and beat until well incorporated. Add the eggs, one at a time, mixing on low speed after each addition.
4. Incorporate the Sour Cream and Vanilla: Mix in the sour cream and vanilla extract until smooth. Do not overmix.
5. Assemble and Bake the Cheesecake Layer: Pour the cheesecake batter over the cooled carrot cake layer in the springform pan. Use a spatula to spread it evenly. Place the springform pan on a baking sheet and bake for 45-50 minutes, or until the center is just slightly jiggly.

3. Cool and Chill the Cake

1. Cool Gradually: Turn off the oven and leave the cheesecake inside with the door slightly ajar for 1 hour. This helps prevent cracks.
2. Chill: Once the cheesecake has reached room temperature, cover it with plastic wrap and refrigerate for at least 6-8 hours, or overnight for the best results.

4. Prepare the Cream Cheese Frosting

1. Beat the Cream Cheese and Butter: In a medium bowl, beat the cream cheese and butter on medium speed until smooth and fluffy.
2. Add Powdered Sugar: Gradually add the powdered sugar, beating until fully incorporated.
3. Add Vanilla and Adjust Consistency: Mix in the vanilla extract and add milk, 1 teaspoon at a time, until the frosting reaches your desired consistency.

5. Assemble and Decorate

1. Frost the Cake: Remove the cheesecake from the springform pan and spread the cream cheese frosting evenly over the top.
2. Add Garnishes: Decorate with chopped nuts, shredded coconut, or carrot curls for a festive touch.
3. Slice and Serve: Use a sharp knife to slice the cake, cleaning the blade between cuts for neat slices.