Prepare the Crust:

1. Preheat the Oven: Preheat your oven to 325°F (160°C). Grease and line the bottom of a 9-inch springform pan with parchment paper for easy removal.
2. Make the Crust: In a medium-sized bowl, combine the digestive biscuit crumbs (or graham cracker crumbs) and brown sugar. Stir in the melted butter until the mixture is well combined and has a sandy texture.
3. Press into Pan: Press the crumb mixture firmly into the bottom of the prepared pan. Use the back of a spoon to create an even layer. Bake in the preheated oven for about 10-12 minutes, until the crust is set and slightly golden. Remove from the oven and set aside to cool.

Make the Cheesecake Filling:

4. Mix the Cream Cheese: In a large mixing bowl, beat the softened cream cheese and mascarpone cheese together using an electric mixer on medium speed until smooth and creamy. Scrape down the sides of the bowl as needed.
5. Add the Sugar: Gradually add the granulated sugar and continue to mix until fully incorporated.
6. Add the Eggs and Vanilla: Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
7. Prepare the Coffee Mixture: In a small bowl, dissolve the instant coffee granules (if using) into the cooled espresso or brewed coffee. Stir to combine.
8. Add Coffee to Filling: Slowly pour the coffee mixture into the cream cheese batter, mixing gently until the coffee flavor is evenly distributed.
9. Thicken with Cornstarch: Sprinkle the cornstarch over the batter and stir gently to incorporate. This will help the cheesecake set to a perfect consistency.

Bake the Cheesecake:

10. Pour into the Pan: Carefully pour the cheesecake filling over the cooled crust in the springform pan. Smooth the top with a spatula to make it even.
11. Bake: Bake for 60 minutes or until the edges are set but the center still slightly jiggles when you tap the pan. The top should be lightly golden.
12. Cool in the Oven: Turn off the oven and leave the cheesecake in the oven with the door slightly ajar for 1 hour. This helps prevent cracks from forming.
13. Chill: After 1 hour, remove the cheesecake from the oven and let it cool to room temperature. Then transfer it to the refrigerator to chill for at least 4 hours or overnight for best results.

Prepare the Topping (Optional):

14. Make the Espresso Martini Topping: In a small bowl, dissolve the instant espresso powder in warm water. Whisk in the heavy cream to create a smooth, creamy espresso topping.
15. Garnish: Once the cheesecake is fully chilled, drizzle the espresso cream over the top of the cheesecake. Optionally, sprinkle with cocoa powder or chocolate shavings for an elegant touch.

Cut and Serve:

16. Serve: Once chilled, carefully remove the cheesecake from the springform pan and transfer it to a serving platter. Slice into 12-16 pieces, depending on your desired serving size.