Preheat your oven to 325°F (160°C).
In a medium bowl, combine graham cracker crumbs, granulated sugar, and melted butter. Mix until well combined.
Press the crumb mixture firmly into the bottom of a 9-inch springform pan to form the crust. Bake for 10 minutes, then remove from the oven and let cool.
In a large mixing bowl, beat the softened cream cheese and peanut butter together until smooth and creamy.
Add the powdered sugar and vanilla extract, mixing until fully incorporated.
Add the eggs one at a time, mixing on low speed until just combined after each addition. Do not overmix.
Pour in the caramel sauce and heavy cream, mixing until smooth.
Pour the cheesecake batter over the cooled crust in the springform pan.
Bake in the preheated oven for 25-30 minutes, or until the edges are set and the center is slightly jiggly.
Turn off the oven and crack the door, allowing the cheesecake to cool in the oven for 1 hour.
Remove the cheesecake from the oven and refrigerate for at least 4 hours, preferably overnight.
Before serving, drizzle additional caramel sauce on top and slice into pieces.