Melt the chopped chocolate and espresso powder using a double boiler, stirring until smooth. Set aside to cool slightly.
In a large mixing bowl or food processor, beat the softened cream cheese until completely smooth.
Add the granulated sugar, brown sugar, and cocoa powder. Mix until creamy.
Beat in the eggs and egg yolks one at a time, mixing just until combined after each addition.
Add the heavy cream and vanilla extract and mix until smooth.
Fold the melted chocolate into the batter using a rubber spatula until fully incorporated.
Pour half of the cheesecake batter over the cooled Oreo crust.
Arrange the fresh raspberries evenly over the batter.
Cover the raspberries with the remaining cheesecake batter, smoothing the top.
Place the springform pan inside a large roasting pan.
Carefully pour hot water into the roasting pan until it reaches about 1 inch up the sides of the springform pan.
Bake for 70 minutes, or until the edges are set and the center still has a slight wobble.
Remove the cheesecake from the water bath and place it on a cooling rack.
Run a thin knife around the inside edge of the pan to help prevent cracking.
Cool completely, then refrigerate for at least 6 hours, preferably overnight.