Preheat the oven to 350F/180C. Line an 8×8-inch baking pan with parchment paper, leaving enough overhang on the sides for lifting the cheesecake out of the pan after baking.
Pulse the Oreos (the whole cookie, with their filling) in a food processor or blender until finely ground. Place the crumbs in a medium bowl and stir in the melted butter. Place crumbs in the pan, and gently press with your fingers to form an even layer. Bake for 8 minutes. Allow to cool while you prepare the cheesecake filling.
Reduce oven temperature to 325F/160C.
In a mixer fitted with the paddle attachment, beat cream cheese on low-medium speed until smooth, about 2 minutes. Add sugar and beat another 2 minutes. Add the eggs, one at a time, until fully combined. Add vanilla and sour cream and beat until incorporated and smooth. Remember to scrape down the sides and the bottom of the bowl. Fold in Oreos.
Pour batter over the cooled Oreo crust and spread evenly. Bake for 30-40 minutes. The center of the cake should be slightly wobbly. Allow the cake to sit at room temperature for 1 hour, then refrigerate for at least 6 hours or until the cake is completely set. Lift the cake out of the pan using the parchment paper and cut into squares.
To drizzle the chocolate: place the melted chocolate into a ziplock bag, and snip a small corner off the corner of the bag. Drizzle chocolate over the cheesecake bars. Chill the bars until ready to serve.
Cheesecake tastes best after 24 hours, so it's best to prepare it a day in advance. It will keep well in an airtight container in the fridge for several days.