Preheat your oven to 350°F (175°C) and grease a 9-inch springform pan.
In a large bowl, beat cream cheese and sugar until smooth. Add flour, eggs, and vanilla extract, mixing until well combined. Set aside.
In another bowl, mix vegetable oil, sugar, eggs, and vanilla until blended. Gradually add flour, baking soda, cinnamon, and salt, then fold in pineapple, grated carrots, coconut, and nuts.
Spread 1.5 cups of carrot cake batter in the bottom of the prepared pan. Spoon half of the cheesecake mixture on top. Repeat layering with remaining carrot cake and cheesecake batter.
Bake in the oven for 50-60 minutes, until set and slightly puffed. A toothpick inserted should come out clean.
Allow the cheesecake to cool on a wire rack until it reaches room temperature, then refrigerate for at least 4 hours.
For the frosting, beat cream cheese and butter until smooth. Gradually add powdered sugar, vanilla, pineapple juice, and salt, mixing until fluffy.
Frost the chilled cheesecake generously and garnish with additional nuts if desired.
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Notes
Store leftovers covered in the refrigerator for up to 5 days. You can also freeze slices for up to 3 months.