Preheat. Preheat the oven to 375°F and lightly grease a 6-inch springform pan.
Make the crust. In a medium bowl, combine the crushed Oreos, sugar, and melted butter. Press the crumb mixture into the pan and bake for 10 minutes. Remove and set aside to cool slightly. Reduce the oven to 350°F.
Melt the chocolate. In a saucepan, combine the milk and chocolate chips and heat on low until the chocolate chips are melted. Remove from heat and stir in the espresso powder. Set aside.
Beat the cream cheese and sugar. In a large bowl, beat together the cream cheese and sugar for about 2 minutes.
Add the eggs. Add the eggs and beat again until well combined.
Add the vanilla and flour. Add the vanilla extract and flour and beat until well combined.
Combine with the chocolate. Fold the melted chocolate mixture into the cream cheese batter until fully combined.
Bake. Pour the batter onto the crust and bake for about 45 minutes, or until a toothpick placed into the edge of the cake comes out clean.
Cool gradually. Turn off the oven and leave the door open several inches, letting the cheesecake cool inside for about an hour.
Chill. Remove, cover, and chill in the refrigerator for another hour, or until ready to serve.
Serve. Top with crushed Oreos and serve.