Preheat oven to 325F (160C). Line a 13x9 baking pan with foil and set aside.
To make the crust, place 25 of your Oreo cookies in a food processor and pulverize until they are fine crumbs. Add butter and salt and pulverize again, until completely combined.
Pour cookie crumb mixture into prepared baking pan and use the back of a spoon to press the crumbs firmly into an even layer. Set aside.
Break your remaining 15 Oreo cookies into pieces -- do not completely pulverize them but break them into fragments (to do this, I place the cookies in a large Ziploc bag and whack them a few times with a rolling pin). Set aside.
In a stand mixer (or in a large bowl with a hand-mixer), cream together softened cream cheese and sugar, scraping down the sides with a spatula occasionally to ensure ingredients are mixed well.
Add sour cream and stir well, pausing once to scrape down the sides and bottom of the bowl.
Add eggs, one at a time, beating until just mixed after each addition (and scraping down the sides after each addition)
Stir in vanilla extract and then use a spatula to stir in cookie pieces.
Spread cheesecake batter evenly over prepared cookie crust. If desired, sprinkle a few additional Oreo pieces over the top of the cheesecake.
Bake on 325F (160C) for 40 minutes, or until center is set (center should bounce back if lightly touched).
Allow to cool to room temperature, and then place in refrigerator for at least 6 hours before cutting and serving.