It's best if it ripens in the refrigerator overnight, so plan on making it a day ahead.
1. Position the rack in the center of the oven and preheat the oven to 350°F. Wrap the outside of a 9-inch springform pan tightly in aluminum foil (this will keep the water in the water bath from seeping into the batter as the cake bakes); set aside.
2. Stir the graham cracker crumbs, melted butter, brown sugar, cinnamon, and salt in a large bowl until the graham cracker crumbs are thoroughly moistened. Pour a little more than half of this mixture into the bottom of the prepared springform pan and press it all the way to edges so that it coats the bottom of the pan. Pour the rest of the mixture around the inner seam of the pan, where the rim meets the bottom; press the crust halfway up the sides of the pan, filling in along the bottom where necessary. Set aside.
3. Beat the cream cheese and granulated sugar in a large bowl with an electric mixer at medium speed until smooth, about 2 minutes. If you rub a small bit between your fingers, you should feel only a few sugar granules. Beat in the peanut butter. Scrape down the sides of the bowl with a rubber spatula, then beat in the eggs one at a time, making sure each is thoroughly incorporated before adding the next. Finally, beat in the sour cream and vanilla.
4. Taking care not to disturb the crust, pour this mixture into the prepared pan. Smooth its top with a rubber spatula. Place the springform pan in a high-sided roasting pan that's large enough to accommodate it comfortably. Fill the larger roasting pan with hot water until it comes about halfway up the outside of the springform pan.
5. Bake until the cheesecake's top is dry and lightly browned and the cake jiggles like a set custard when tapped, about 1 1/2 hours. Cool in the pan for 15 minutes, then remove the springform pan from the water bath and cool it completely to room temperature on a wire rack.
6. Remove the foil and cover the pan with plastic wrap, taking care not to press the wrap onto the surface of the cheesecake. Refrigerate overnight.
7. Unlatch the sides and transfer to a serving platter. If desired, run a long knife between the pan's bottom and the cake, then gently slide the cake onto the serving platter.