Prepare a water bath by placing a 9x13-inch (or similar size) pan filled with an inch of water on the lower rack of your oven. Position the rack above it for the cheesecake. Preheat the oven to 300°F (150°C). Line the bottom of a 9-inch springform pan with parchment paper.

In a mixing bowl, beat softened cream cheese until creamy. At low speed, gradually add sugar, salt, and flour until fully blended. Mix in the vanilla extract and sour cream until smooth, then add eggs one at a time, mixing well after each addition. Pour the batter into the prepared pan and place it on the rack above the water bath. Bake for 45 minutes until set, with a slight jiggle in the center. Turn off the oven and leave the cheesecake inside for 30 minutes with the door slightly ajar. Cool on the counter before chilling in the freezer for 2-3 hours, or refrigerate for 5-6 hours or overnight if not in a rush.

Preheat the oven to 350°F (175°C). Line the bottoms of two 9-inch round cake pans with parchment or wax paper, grease, and flour the pans thoroughly to prevent sticking. In a bowl, whisk together the flour, baking soda, baking powder, cinnamon, and salt for 30 seconds and set aside.

In the mixer bowl, combine sugar, eggs, oil, and vanilla. Beat on medium speed for 2-3 minutes until the mixture is light and well combined. Stir in the dry ingredients with a spoon until just moistened, then fold in grated carrots, pecans, coconut, and drained pineapple. Divide the batter evenly between the prepared pans and bake for 35-40 minutes or until a toothpick inserted in the center comes out clean. Avoid opening the oven door during baking to prevent sinking. Cool the cakes in their pans for 10 minutes before transferring them to a wire rack to cool completely.

Slice the butter and add it to your mixer bowl. Beat on medium speed until smooth. Add softened cream cheese in pieces, beating until fully combined. Add vanilla and gradually mix in powdered sugar, covering the bowl with a towel to minimize the powdered sugar cloud. Increase the speed and beat until fluffy, but do not overbeat as it will become too soft. If the frosting is too soft, refrigerate briefly. This frosting pipes best when slightly chilled. It can be made ahead and refrigerated; soften slightly before remixing for use.

Place one carrot cake layer on your serving plate and spread a thin layer of frosting on top. To remove the cheesecake, run a hot, thin knife around the edges, release the springform, and invert the cheesecake onto the frosted carrot layer. Remove the pan bottom and parchment paper. Frost the cheesecake layer lightly before topping with the second carrot cake layer. If the cheesecake layer is slightly larger, trim the edges with a hot knife. Frost the assembled cake as desired, chilling briefly if layers begin to slip. Decorate with your preferred piping style; we used a 1M tip for a shell border. Due to the cream cheese components, refrigerate the cake until about an hour before serving.