Place the softened cream cheese and granulated sugar in a large bowl. Using a stand mixer fitted with the paddle attachment or a handheld electric mixer, beat on medium-high speed for about 2 minutes, until completely smooth and creamy.
Add the sour cream and mix until incorporated. Follow with the peanut butter, vanilla extract, and salt, beating until the filling is smooth and everything is evenly combined.
Reduce the mixer to medium speed and add the eggs one at a time. Mix just until each egg disappears into the batter before adding the next. Once the third egg has been incorporated, stop mixing. Do not worry if you see a few tiny lumps. Give the mixture several gentle turns with a whisk by hand, paying particular attention to the bottom of the bowl, to remove any larger pockets of unmixed ingredients.
Pour the peanut butter cheesecake mixture over the baked Oreo crust. The crust can still be slightly warm at this stage. Use a rubber spatula or the back of a spoon to spread the filling into an even layer. It will look quite thick, which is exactly what you want.
Bake for 35 to 38 minutes, or until the cheesecake looks set across the surface and the edges have developed a light brown color. A few small cracks around the edges are perfectly normal. The cheesecake will puff up while baking and settle slightly as it cools.
Place the pan on a wire rack and allow the cheesecake to cool at room temperature for 1 hour. Transfer it to the refrigerator and chill for at least 3 hours, or as long as 1 day, before adding the chocolate topping.
If you need to speed things up, you can chill the cheesecake in the freezer for about 2 hours, or until it is thoroughly cold. For longer refrigeration, loosely cover the pan with aluminum foil after the first 3 to 4 hours.