Preheat oven to 350°F. Line the bottom of a 9-inch springform pan with foil and spray lightly with nonstick cooking spray.
In a medium bowl, combine graham cracker crumbs, butter, granulated sugar and pumpkin pie spice. Press onto bottom and 1 inch up side of prepared pan. Bake for 7 to 8 minutes. Cool on wire rack for about 10 minutes.
Begin to boil a large pot of water for the water bath.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with an electric mixer, combine cream cheese, granulated sugar and brown sugar until fluffy; about 3 minutes. Add in eggs, pumpkin and heavy cream, mix until fully incorporated; scraping down the sides of the bowl as needed. Finally, add in vanilla and pumpkin pie spice and mix until well combined.
Pour batter into prepared crust. Place pan into a larger pan and pour boiling water into the larger pan until halfway up the side of the cheesecake pan.
Bake 60 minutes, the edges will appear to be set, but the center will still have some jiggle to it. At this point, close the oven door, turn the heat off, and let rest in the cooling oven for one hour. After one hour has passed, carefully remove the cheesecake from the water bath and place on a cooling rack to cool completely. Once the cake is completely cooled, place it into the refrigerator for at least 6 hours.