Prepare the oven and pan: Preheat oven to 325°F (160°C). Grease a 9-inch springform pan and wrap the bottom with aluminum foil to prevent any leaking during baking. This double protection ensures your cheesecake bakes perfectly without any messy drips in your oven.
Make the crust: In a medium bowl, thoroughly combine the chocolate cookie crumbs, sugar, and melted butter until the mixture resembles wet sand. Press this mixture firmly into the bottom of the prepared springform pan, creating an even layer. Bake for 10 minutes to set the crust. Remove from the oven and allow to cool slightly while preparing the filling.
Prepare the filling: In a large mixing bowl, beat the softened cream cheese and granulated sugar together until completely smooth and fluffy, about 2-3 minutes. Add cocoa powder and beat until fully incorporated. Next, add the sour cream, followed by eggs one at a time, mixing just until each is incorporated. Stir in vanilla extract and melted chocolate, mixing gently until the batter is uniform but taking care not to overmix.
Bake the cheesecake: Pour the chocolate filling over the prepared crust and smooth the top with a spatula. Bake for 55-65 minutes, or until the center is just set but still slightly jiggly. Turn off the oven, crack the door open, and allow the cheesecake to cool gradually for 1 hour inside the cooling oven to prevent cracking. After this initial cooling, refrigerate for at least 4 hours or overnight.
Make the coconut-pecan topping: In a medium saucepan, combine evaporated milk, brown sugar, egg yolks, and butter. Cook over medium heat, stirring constantly with a wooden spoon or silicone spatula, until the mixture thickens to a custard-like consistency, about 8-10 minutes. Remove from heat and stir in the vanilla extract, shredded coconut, and chopped pecans. Allow the topping to cool completely.
Finish the cheesecake: Once the topping has cooled and the cheesecake is thoroughly chilled, spread the coconut-pecan mixture evenly over the top of the cheesecake. Remove the sides of the springform pan before serving for an elegant presentation.