Preheat the oven.

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

In another bowl, combine all-purpose flour, 1 cup granulated sugar, brown sugar, baking powder, baking soda, cinnamon, nutmeg, and salt.

In a separate bowl, beat 2 eggs and vegetable oil; add grated carrots and walnuts (if using).

Mix the dry ingredients with the wet ingredients until just combined.

In a new bowl, beat cream cheese, 1/2 cup granulated sugar, vanilla extract, and 2 eggs until smooth. Add sour cream and mix.

Layer the carrot cake mixture over the crust, then add the cheesecake layer on top.

Bake in the preheated oven for 60 minutes. Allow to cool before slicing.