Preheat the oven to 350 degrees Fahrenheit (180 degrees C) and place the oven rack in the center of the oven. Butter or spray with a nonstick vegetable spray, three - 8 x 2 inch deep round baking pans. Line the bottoms of the pans with parchment paper and set aside. In a small heatproof bowl, place the finely chopped unsweetened chocolate and cocoa powder. Add the hot coffee and stir until the mixture is melted and smooth. Set aside to cool to room temperature. To a medium bowl, add the flour, baking powder, baking soda, and salt. Stir quickly with a fork to combine. In the bowl of an electric mixer, fitted with a paddle attachment (a hand mixer works here as well) over medium/high speed, beat the butter and sugar until the mixture is light and fluffy, about 3-4 minutes. Add the eggs one at a time beating well after each addition. Stop the mixer and scrape the sides of the bowl. Turn the mixer to low/medium speed. Add the vanilla extract and melted chocolate mixture and beat to combine. The mixture should look sort of billowy, like a mousse.
Reduce the speed to low. Add the flour mixture alternating with the milk, beginning and ending with the flour mixture. Beat until the ingredients are incorporated, but be sure not to over mix or the cake will be tough.
Divide the batter evenly between the three prepared pans. Bang the pans on your counter to smooth out the batter and remove any air bubbles. Place in the oven and bake for about 30 - 35 minutes or until a toothpick inserted in the center comes out clean and the cake starts to separate from the sides.
Remove pans from oven and place on a wire rack to cool for about 8-10 minutes. Carefully invert the cakes (one at a time) over the wire rack and lift the pan. Remove the parchment paper and then, to prevent cracks, invert the cake onto a wire rack so that tops are right side up. Allow the cakes to cool completely. As the cake bakes, make and chill the pumpkin cheesecake filling.