Preheat oven to 375°F. Spray a 9-inch springform pan with non-stick cooking spray; optionally line the bottom with parchment and spray the parchment as well.
Make the cake layer: place 4 oz bittersweet chocolate chips and 1/2 cup butter in a microwave-safe bowl. Microwave in 20-second increments, stirring between each, until completely melted and smooth.
Stir 3/4 cup granulated sugar into the melted chocolate-butter mixture. Add 3 room-temperature eggs one at a time, stirring until each is incorporated. Stir in 1 teaspoon vanilla extract.
Sift 1/2 cup unsweetened cocoa powder into the batter, add a pinch of salt, and gently stir to combine. Fold in 1 1/2 oz dark chocolate chips.
Pour the cake batter into the prepared springform pan and smooth the top. Bake 20–25 minutes, or until the cake is just set (a toothpick inserted near the center should come out with a few moist crumbs). Remove from oven and cool completely in the pan. Reduce oven temperature to 325°F.
While the cake cools, melt the cheesecake chocolate: place 1 cup bittersweet chocolate chips and 1 cup dark chocolate chips in a small glass bowl. Microwave in 20-second increments, stirring each time, until melted and smooth. Set aside to cool slightly.
Make the cheesecake filling: in a large bowl or the bowl of a stand mixer, beat 32 oz cream cheese (room temperature) for about 30 seconds until smooth. Scrape the bowl, then add 1 cup granulated sugar, 1/4 cup unsweetened cocoa powder, and 1 teaspoon vanilla extract; mix until combined.
Add the slightly cooled melted chocolate, 1/4 cup freshly brewed espresso (cooled to room temperature), and 1/4 cup room-temperature heavy cream to the cream cheese mixture. Mix until smooth, scraping the sides and bottom of the bowl.
In a small bowl, beat 4 large room-temperature eggs until well mixed. With the mixer on low, slowly pour the eggs into the cream cheese mixture and stop mixing as soon as the eggs are incorporated. Scrape the bowl and fold gently if needed so the batter is completely smooth.
Tap the bowl on the counter for 30–45 seconds to release air bubbles (you should see bubbles popping on the surface). Pour the cheesecake filling into the springform pan over the cooled cake layer and smooth the top.
Bake the cheesecake at 325°F for 30 minutes. After 30 minutes, reduce the oven temperature to 250°F and bake an additional 45 minutes. When the time is up, turn the oven off and leave the cheesecake inside with the door closed for 30 minutes (carryover cooking).
After 30 minutes, crack the oven door and let the cheesecake cool slowly for 1 hour. Remove from oven and bring to room temperature on the counter for 3–4 hours. Once at room temperature, cover loosely with plastic wrap and refrigerate while you prepare the mousse layer.
Make the chocolate for the mousse: place 10 oz semi-sweet chocolate chips in a microwave-safe bowl and microwave in 20-second intervals, stirring between each, until melted and smooth. Let cool slightly.
In a separate bowl, beat 8 oz cream cheese (room temperature) until smooth. Add the melted semi-sweet chocolate and mix until combined.
In a chilled mixing bowl, whip 1 cup cold heavy cream with 1 tablespoon powdered sugar, 1/4 cup unsweetened cocoa powder, and 1 teaspoon vanilla extract until stiff peaks form.
Fold the whipped cream into the chocolate–cream cheese mixture a few spoonfuls at a time until no streaks remain and the mousse is uniform.
Remove the chilled cheesecake from the refrigerator and spread the chocolate mousse evenly over the top. Cover loosely with plastic wrap and chill for at least 1 1/2 hours.
Make the ganache: microwave 3/4 cup heavy cream in a small glass bowl until very hot (about 1 minute). Add 8 oz semi-sweet chocolate chips to the hot cream, let stand for 5 minutes, then stir until smooth and glossy.
Remove the cheesecake from the refrigerator and pour the ganache over the top, allowing it to drip naturally over the edges. Smooth gently with an offset spatula if desired. Return the cheesecake to the refrigerator (uncovered) so the ganache can set.
Make the chocolate shavings: using a knife, vegetable peeler, or other tool, shave or break 3.5 oz dark chocolate bar into small pieces or shavings.
Pile the chocolate shavings in the center of the chilled cheesecake. Serve immediately or cover and refrigerate until ready to serve.