Preheat oven to 350°F (180°C). Spray a 13x9-inch baking pan with cooking spray. Line pan with parchment paper, letting excess extend almost to top of pan.

Let Black Cocoa Shortcrust stand at room temperature until slightly softened, 10 to 15 minutes, if necessary. Transfer dough to prepared pan, pressing to cover bottom of pan. Top with a piece of parchment paper, letting excess extend over edges of pan. Add pie weights.

Bake until edges are set and crust is fragrant, 15 to 20 minutes. Carefully remove parchment and weights. Let cool in pan on a wire rack for 25 minutes. Leave oven on.

In the bowl of a stand mixer fitted with the paddle attachment, beat 2 packages (454 grams) cream cheese at medium speed until smooth and creamy, 1 to 2 minutes, stopping to scrape sides of bowl.

In a small bowl, stir together liqueur and instant coffee until granules dissolve. Add liqueur mixture, ¾ cup (150 grams) sugar, flour, ¾ teaspoon (3 grams) vanilla, and salt to cream cheese; beat until well combined, 1 to 2 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating just until combined after each addition. Pour cream cheese mixture onto prepared crust, spreading into an even layer with a small offset spatula. Gently tap sides of pan several times to release any air bubbles, popping any that rise to the surface with a wooden pick.

Bake until edges are set, top has a dulled finish, center is almost set, and an instant-read thermometer inserted in center registers 150°F (66°C) to 155°F (68°C), about 20 minutes. Immediately run a knife around pan to loosen bars from parchment; let cool in pan on a wire rack for 1½ to 2 hours.

Clean bowl of stand mixer and paddle attachment. Using the paddle attachment, beat remaining 1 package (226 grams) cream cheese at medium speed until smooth and creamy, 1 to 2 minutes, stopping to scrape sides of bowl. Add cream, remaining ¼ cup (50 grams) sugar, and remaining 2¼ teaspoons (9 grams) vanilla; beat until smooth and well combined. Transfer ¼ cup (about 54 grams) cream cheese mixture to a small bowl; stir in black cocoa.

Spoon and spread remaining cream cheese mixture onto cooled cheesecake layer in pan. Drop small dollops of black cocoa mixture on top of cream cheese mixture; using a wooden pick, swirl as desired, being careful not to hit cheesecake layer underneath. Refrigerate for at least 1 hour or up to overnight, loosely covering with foil only when completely cool to prevent condensation from forming on top.

Using excess parchment as handles, remove from pan. Using a warm, dry knife, cut into bars.