Preheat the oven to 300°F (150°C). Wrap a 9-inch springform pan in two layers of aluminum foil (bottom and sides) to seal it against water.
Combine the graham crackers (or digestive biscuit), desiccated coconut, and melted butter in a bowl until evenly moistened. Press the mixture firmly and evenly into the bottom of the prepared springform pan to form the crust. Refrigerate the crust while you prepare the filling.
In a large bowl, beat the cream cheese until smooth. Add the fine sugar and continue beating until creamy. Add the eggs one at a time, beating well after each addition. Add the whipping cream and beat until the mixture is thick and homogeneous. Stir in the cornstarch until fully incorporated.
Divide the cheesecake batter into three equal portions (by volume or weight).
Prepare the water bath: place the wrapped springform pan on a baking sheet or directly into a large roasting pan that can hold hot water. Have hot water ready to pour into the roasting pan after the springform is placed inside.
To the first portion of batter, stir in the melted dark chocolate and the sieved cocoa powder until smooth and evenly combined. Pour this chocolate batter over the chilled crust and smooth the top.
Place the springform pan into the roasting pan, pour hot water into the roasting pan until it reaches about halfway up the sides of the springform (take care handling hot water), and transfer to the oven. Bake for 30 minutes.
While the first layer bakes, stir the melted white chocolate and the vanilla extract into the second portion of batter until smooth.
After the first 30 minutes, remove the roasting pan from the oven (use oven mitts), carefully lift the springform pan from the water just enough to pour off or top up water as needed, then gently pour the white chocolate layer over the baked chocolate layer, smoothing the top. Return the springform pan to the roasting pan, replenish hot water if necessary so it again reaches about halfway up the sides, and bake for another 30 minutes.
Dissolve the instant coffee granules in the hot water, then stir the coffee mixture and the Kahlua into the third portion of batter until evenly combined.
After the second 30-minute bake, remove the roasting pan from the oven, gently pour the coffee batter over the second layer, top up the hot water in the roasting pan if needed, and return to the oven. Bake for a final 30 minutes.
When the final 30-minute bake is complete, turn off the oven, crack the oven door open, and leave the cake inside for about 30 minutes to cool gradually.
Carefully remove the springform pan from the roasting pan and discard the hot water. Let the cheesecake cool completely on a wire rack, then refrigerate (still in the springform) for at least 6 hours or overnight to set.
Remove the foil and the springform, slice, and serve with strawberries.