Creating the Crimson Choco-Berry Rhapsody Cheesecake is a delightful process; just follow these steps:

1. Preheat the Oven: Preheat your oven to 325°F (160°C). Prepare a 9-inch springform pan by greasing it lightly.

2. Make the Crust: In a mixing bowl, combine the chocolate cookie crumbs, melted butter, and granulated sugar. Mix until well combined and press firmly into the bottom of the prepared springform pan. Bake for 10 minutes, then set aside to cool.

3. Prepare the Cheesecake Filling: In a large mixing bowl, beat the softened cream cheese and granulated sugar until smooth and creamy. Add the vanilla extract and mix well.

4. Add Eggs: Add the eggs one at a time, beating well after each addition. Make sure to scrape down the sides of the bowl to ensure everything is mixed evenly.

5. Incorporate Sour Cream and Chocolate: Gently fold in the sour cream and melted chocolate until fully combined and smooth.

6. Pour Filling Over Crust: Pour the cheesecake filling over the cooled chocolate crust, smoothing the top with a spatula.

7. Bake: Place the cheesecake in the preheated oven and bake for 55-60 minutes. It should be set around the edges, but the center will slightly jiggle.

8. Cool Down: Turn off the oven and leave the cheesecake inside for an additional hour to cool gradually, then remove from the oven and let it cool completely at room temperature. Once cooled, refrigerate for at least 1-2 hours.

9. Prepare the Berry Topping: In a saucepan over medium heat, combine the mixed berries, sugar, and lemon juice. Cook for about 5 minutes until the berries release their juices.

10. Thicken Sauce: Stir the cornstarch mixture into the berry mixture and continue to cook for another minute until thickened. Remove from heat and let cool to room temperature.

11. Assemble the Cheesecake: After the cheesecake has cooled, remove it from the springform pan. Top it with the berry mixture, spreading it evenly across the surface.