Preheat oven to 175°C (350°F). Grease a 9-inch springform pan.
In a large bowl, whisk flour, sugar, baking soda, baking powder, cinnamon, nutmeg, and salt.
In another bowl, beat eggs with oil. Fold in grated carrots, pineapple, and nuts. Combine wet and dry mixtures to make the carrot cake batter.
For the cheesecake layer, beat cream cheese until smooth. Add sugar, eggs, and vanilla; mix until creamy.
Spread half the carrot cake batter into the pan. Add the cheesecake mixture, then top with remaining carrot cake batter.
Bake for 55–65 minutes, until set. Cool completely in the pan, then chill for at least 2 hours.
For frosting: Beat cream cheese and butter until fluffy. Add powdered sugar and vanilla, mixing until smooth.
Frost the cake and finish with walnuts, shredded carrots, or your favorite carrot cake decoration.