Preheat the oven to 325°F (163°C).
In a medium bowl, combine graham cracker crumbs, 1/4 cup granulated sugar, and melted butter. Mix until crumbs are evenly coated.
Press the crumb mixture firmly into the bottom of a 9-inch springform pan to form the crust. Set aside.
In a large mixing bowl, beat the softened cream cheese until smooth and creamy using an electric mixer on medium speed.
Add 1 cup granulated sugar and 1/4 cup brown sugar to the cream cheese and beat until well combined.
Add the eggs one at a time, beating on low speed after each addition until just combined.
Mix in vanilla extract, sour cream, and heavy cream until smooth.
In a separate bowl, combine grated carrots, chopped walnuts, crushed pineapple, cinnamon, nutmeg, ginger, salt, and flour. Stir to combine.
Fold the carrot mixture gently into the cream cheese batter until evenly distributed.
Pour the batter over the prepared crust in the springform pan and smooth the top with a spatula.
Place the springform pan on a baking sheet and bake in the preheated oven for 60 to 70 minutes, or until the center is almost set but still slightly jiggly.
Turn off the oven and leave the cheesecake inside with the door slightly open for 1 hour to cool gradually.
Remove the cheesecake from the oven and let it cool completely at room temperature.
Refrigerate the cheesecake for at least 4 hours or overnight to set fully.
Prepare the cream cheese frosting by beating together softened cream cheese and butter until smooth.
Gradually add powdered sugar and vanilla extract, and beat until creamy and spreadable.
Once the cheesecake is chilled, remove it from the springform pan and spread the cream cheese frosting evenly over the top.
Slice and serve chilled.