Place cream cheese in food processor and process on low. Process for 15 seconds. Increase the speed to high and process for 5 seconds until smooth.
Add sugar and process on low until combined.
Add flour, yogurt, vanilla and milk and process on low until smooth.
Add eggs and process on low until completely incorporated.
Add cooled, melted chocolate and process on low just until combined and the filling is uniform color. No white streaks should remain.
Pour the batter over baked crust. Tap the roasting pan on the counter few times (gently) to release any air bubbles from the batter.
Place the pan with the springform pan in the oven. Pour enough water into the roasting pan to come at least 1 inch up the sides of the springform pan but not over the foil.
Bake 1 hour and 20 minutes. Replace water after first 50 minutes of baking.
When the times is up, turn of the oven leaving the cheesecake inside for one hour. Leave the oven door slightly ajar.
Cool the cheesecake completely on the counter.
Refrigerate any leftovers for up to 5 days in closed container.