Preheat the oven and prepare the springform pan.

In a bowl, combine graham cracker crumbs, 1/4 cup granulated sugar, and melted butter. Press mixture into the bottom of the pan.

In a separate bowl, mix flour, 1 cup granulated sugar, brown sugar, baking powder, baking soda, ground cinnamon, ground nutmeg, and salt.

Add vegetable oil, eggs, grated carrots, and walnuts (if using) to the dry ingredients. Mix until combined.

Pour the carrot cake batter over the crust in the pan.

In another bowl, beat softened cream cheese until smooth. Add sour cream, 1/2 cup granulated sugar, and vanilla extract; mix until incorporated.

Add 2 eggs into the cream cheese mixture and beat until combined.

Pour the cream cheese mixture over the carrot cake batter in the pan.

Bake in the preheated oven for 60 minutes or until set.

Let the cheesecake cool before frosting.

In a bowl, beat softened cream cheese and unsalted butter until smooth. Gradually add powdered sugar and vanilla extract, mixing until fluffy.

Frost the cooled cheesecake with cream cheese frosting.