Step 1: Preheat oven to 325°F (160°C). Wrap the bottom and sides of a 9-inch springform pan with heavy-duty aluminum foil to prevent water from entering during baking (if using a water bath).
Step 2: For the crust, combine graham cracker crumbs, ¼ cup granulated sugar, and melted butter in a medium bowl. Press mixture evenly into the bottom of the prepared springform pan. Bake for 10 minutes. Remove from oven and let cool slightly.
Step 3: In a large bowl, using an electric mixer on medium speed, beat softened cream cheese until smooth and creamy. Add peanut butter and beat until fully incorporated and smooth.
Step 4: Gradually add 1 cup granulated sugar and flour, beating on low speed until just combined, scraping down the sides of the bowl as needed.
Step 5: Beat in vanilla extract. Add eggs one at a time, beating on low speed after each addition just until the yolk disappears. Do not overmix.
Step 6: Gently fold in the melted and slightly cooled white chocolate until streaks are almost gone. Pour the cheesecake batter over the cooled crust in the springform pan.
Step 7: Prepare a water bath: Place the springform pan into a larger roasting pan. Pour hot water into the roasting pan, reaching halfway up the sides of the springform pan.
Step 8: Carefully transfer the roasting pan to the preheated oven. Bake for 1 hour 15 minutes, or until the edges are set and the center still has a slight jiggle. Do not overbake.
Step 9: Turn off the oven, prop the door open slightly, and let the cheesecake cool in the water bath inside the oven for 1 hour. This slow cooling helps prevent cracks.
Step 10: Carefully remove the springform pan from the water bath and the foil. Let cool completely on a wire rack. Once cool, cover loosely with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, for best texture and flavor.
Step 11: To serve, run a thin knife around the edge of the pan before releasing the springform. Garnish as desired, perhaps with whipped cream (beat heavy cream and powdered sugar until soft peaks form), chocolate drizzles, or chopped peanuts.