1. Preheat oven to 350°F (175°C). Grease two 9-inch cake pans; line with parchment and grease the parchment.
2. Make carrot cakes: sift or whisk the flour, sugar, salt, baking soda, and cinnamon together in a large bowl. Add the oil, eggs, and vanilla; beat until well combined. Stir in the nuts, coconut, pureed carrots, and pineapple.
3. Pour evenly into the two prepared pans. Bake for 40–50 minutes, until the edges pull away from the sides and a toothpick inserted in the center comes out clean. Cool for 10 minutes, then turn out onto wire racks and cool completely (about 3 hours) before assembling.

TO MAKE THE CHEESECAKE LAYER:

1. Wrap the outside of a 9-inch springform pan tightly with heavy-duty foil. Line with a parchment round. Preheat oven to 350°F (175°C).
2. Gently melt the white chocolate in a microwave in short bursts, stirring between each, until smooth. Set aside to cool slightly.
3. Using the paddle attachment on a stand mixer, beat the cream cheese, mascarpone, and sugar until smooth. Add the eggs one at a time, beating just until blended after each. Mix in the flour and vanilla, then fold in the melted white chocolate.
4. Spread the batter evenly in the prepared springform pan. Place in a large roasting pan and pour hot water into the roasting pan to come halfway up the sides of the springform.
5. Bake until the center moves only slightly when the pan is gently shaken, about 1 hour. Transfer to a rack; cool 1 hour. Chill overnight. (Can be made 2 days ahead.)

TO MAKE THE ICING:

1. Beat the cream cheese, mascarpone, and butter together until smooth. Sift in the powdered sugar and mix until no lumps remain. Beat in the vanilla.

TO ASSEMBLE:

1. Place one carrot cake layer on a serving plate, rounded side down. Spread a thin layer of icing on top. Set the chilled cheesecake (remove parchment) on top, then add the second carrot cake layer, rounded side down.
2. Frost the entire cake and press the chopped toasted nuts onto the sides if desired. Bring to room temperature before serving.