Preheat oven to 325°F (163°C) and grease a 9-inch springform pan with butter or non-stick spray.
Combine finely crushed Oreo cookies and melted butter in a medium bowl; press the mixture firmly into the bottom of the prepared springform pan.
Bake the crust for 10 minutes, then remove from the oven and set aside to cool.
In a large mixing bowl, beat the cream cheese and granulated sugar together until smooth and creamy.
Add sour cream and vanilla extract, mixing until fully incorporated.
Add eggs one at a time, beating on low speed after each addition just until combined to prevent excess air bubbles.
Fold in the 12 coarsely chopped Oreo cookies manually using a rubber spatula.
Pour the cheesecake batter over the cooled crust and smooth the surface with a spatula.
Bake for 55 to 65 minutes, or until the edges are set and the center has a slight jiggle.
Turn off the oven and leave the cheesecake inside with the door slightly ajar for 60 minutes to cool gradually.
Transfer the cheesecake to the refrigerator and chill for at least 6 hours, preferably overnight.
Prepare the ganache by heating heavy cream until simmering, then pouring it over the chopped semi-sweet chocolate; let sit for 5 minutes before whisking until smooth.
Spread the ganache over the chilled cheesecake and garnish the perimeter with halved Oreo cookies.