Place a rack in middle of oven; preheat to 400°.

Lightly dampen two 16x12" sheets of parchment paper and crumple tightly. Smooth out parchment and line pan with parchment, overlapping as needed to ensure it covers sides.

Combine ¼ cup instant espresso powder and 2 Tbsp. Dutch-process cocoa powder in 2 Tbsp. hot water in a medium bowl, smashing and stirring with a rubber spatula, until dissolved and smooth; set espresso mixture aside.

Beat four 8-oz. packages cream cheese, room temperature, 2 cups (400 g) sugar, ¼ cup (31 g) all-purpose flour, 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt, and 1 Tbsp. vanilla bean paste or vanilla extract in the bowl of a stand mixer fitted with the paddle attachment on medium-low speed until sugar is dissolved and mixture is very smooth, about 2 minutes.

Increase speed to medium and add 6 large eggs, two at a time, beating until incorporated after each addition before adding more, about 45 seconds total.

Scrape down sides of bowl, then reduce speed to medium-low. Add two 8-oz. containers mascarpone, room temperature, 1 cup heavy cream, and 2 Tbsp. Marsala or dark rum and beat until combined and smooth, about 1 minute.

Transfer half of batter to bowl with reserved espresso mixture; stir with rubber spatula until incorporated.

Alternating between batters, scrape large dollops into prepared pan. Shake pan gently to level surface.

Bake cheesecake until deeply golden brown on top and still very jiggly in the center, 50–55 minutes.

Let cheesecake cool in pan on baking sheet 10 minutes. Transfer to refrigerator and chill until cold, at least 4 hours.

Beat remaining one 8-oz. container mascarpone, room temperature, 1 cup heavy cream, 2 Tbsp. Marsala or dark rum, 2 Tbsp. sugar, and ¼ tsp. Diamond Crystal or Morton kosher salt in the clean bowl of stand mixer fitted with the whisk attachment on medium speed until medium-firm peaks form, about 2 minutes.

Spoon over chilled cheesecake, swirling as desired. Chill until topping is set, about 15 minutes.

To serve, dust top of cheesecake with cocoa powder. Remove sides from pan and carefully peel away parchment paper from cheesecake. Slice into wedges.