In a large mixing bowl, beat the softened cream cheese, granulated sugar, and brown sugar until smooth and creamy.
Add the eggs and beat until combined.
Add the pumpkin puree, evaporated milk, cinnamon, and nutmeg. Mix until the filling is smooth and well combined.
Pour the pumpkin cheesecake filling into the cooled graham cracker crust.
Bake at 350°F for 55–60 minutes, or until the edges are set and the center still has a slight jiggle.
Remove the cheesecake from the oven and allow it to cool completely on a wire rack.
Refrigerate for at least 4 hours, preferably overnight, before slicing and serving.