Preheat oven to 325°F (163°C). Grease a 9-inch springform pan and wrap the bottom in two layers of foil.
Crush Oreos into fine crumbs using a food processor. Mix with melted butter and press firmly into the bottom of the pan.
Bake the crust for 10 minutes, then set aside to cool.
In a large bowl, beat cream cheese until smooth and creamy. Add sugar, cocoa powder, and vanilla, mixing well.
Add melted chocolate and sour cream. Beat until combined.
Add eggs one at a time, beating on low and scraping down the sides.
Pour filling over cooled crust. Tap pan on counter to release air bubbles.
Place pan in a larger roasting pan and fill outer pan with hot water halfway up the sides.
Bake for 55–65 minutes, until center is almost set. It should still jiggle slightly.
Turn off oven, crack the door, and let cheesecake sit inside for 1 hour.
Remove from oven, cool to room temp, then chill at least 6 hours or overnight.