Preheat oven to 325. Lightly grease 13 x 9 baking pan with vegetable shortening.
Measure out 1/2 cup of cake mix and set aside for filling.
Place remaining cake mix, melted butter, and 1 egg in mixer bowl. Blend with mixer on low speed for 2 minutes. Stop machine and scrape down sides of bowl. The batter should come together in a ball. With your fingertips, pat the batter evenly over bottom and 1 inch up sides of prepared pan, smoothing it out with your fingers until the top if smooth. Set pan aside.
For filling, place cream cheese and condensed milk in mixing bowl that was used to make the crust, and with the same beaters (no need to clean them). Blend with mixer on low speed just until combined, 30 seconds. Stop machine and add reserved cake mix, remaining 3 eggs, sour cream, vanilla, and coffee powder and beat on medium speed for 1 minute. Stop machine an scrape down sides of bowl. Remove 1 cup of batter, place it in small bowl, and whisk in the melted chocolate until the mixture is well combined. Set the chocolate mixture aside.
Pour the coffee-flavored filling onto the crust and spread with rubber spatula so that the filling covers the entire surface and reaches the sides of the pan. With a tablespoon, drop chocolate mixture on top of the filling. With a dinner knife, swirl the chocolate mixture around in the batter to create a marbled effect. Place pan in the oven. Bake cheesecake until it looks shiny and center no longer jiggles when you shake the pan, 35-40 minutes. Remove pan from oven and place it on wire rack to cool, 30 minutes. Lightly cover pan with plastic wrap and place pan in refrigerator to chill for at least 1 hour. Cut into squares and serve.