Prepare the crust: Preheat oven to 325°F (163°C). Combine chocolate cookie crumbs and melted butter in a bowl. Press the mixture firmly into the bottom of a 9-inch springform pan. Bake for 8–10 minutes, then set aside to cool.
Make the cheesecake filling: In a large mixing bowl, beat the cream cheese, granulated sugar, and brown sugar until smooth and creamy. Add sour cream and melted chocolate, mixing until fully combined.
Add eggs and vanilla: Beat in eggs one at a time, followed by the vanilla extract. Mix until just combined — do not overmix to prevent cracks.
Bake the cheesecake: Pour the filling over the cooled crust and smooth the top. Bake for 55–65 minutes, or until the edges are set and the center is slightly jiggly.
Cool the cheesecake: Turn off the oven, crack the door open, and let the cheesecake rest inside for 1 hour. Then refrigerate for at least 4 hours or overnight.
Make the topping: In a saucepan over medium heat, whisk together evaporated milk, brown sugar, egg yolks, and butter. Cook for 8–10 minutes, stirring constantly, until thickened and golden. Remove from heat and stir in vanilla, toasted coconut, and pecans.
Assemble: Once the cheesecake is chilled, spread the coconut-pecan topping evenly over the top.
Serve: Slice with a warm knife for clean cuts and enjoy chilled.