Place the graham crackers in a zip-top bag and crush them into fine crumbs using a rolling pin or heavy bottle. Transfer the crumbs to a bowl and stir in the melted butter until evenly coated.
Press the crumb mixture evenly into the bottom of a lined springform pan, creating a firm crust. Chill in the refrigerator for about 15 minutes to set.
In a large mixing bowl, beat the softened cream cheese with a whisk until silky smooth and free of lumps, about 2 minutes.
Fold in the peanut butter and sifted powdered sugar, mixing until fully combined and fragrant—this gives the filling its rich, salty flavor.
In a separate chilled bowl, whip the heavy cream with a whisk until soft peaks form, about 3-4 minutes. The cream should hold gentle peaks and be slightly fluffy.
Gently fold the whipped cream into the peanut butter mixture, using a spatula to keep the batter light and airy. Be careful not to deflate the mixture.
Pour the creamy filling over the chilled crust, smoothing the top with a spatula. Cover loosely with plastic wrap and refrigerate for at least 4 hours or overnight to set.
Once set, run a warm knife around the edges of the cheesecake and carefully release the springform. Slice with a warm knife for clean cuts.
Garnish with chopped peanuts or chocolate shavings if desired, then serve chilled and enjoy the luscious, peanutty goodness!