Step 1
Place a rack in middle of oven; preheat to 400°. Lightly dampen two 16×12″ sheets of parchment paper and crumple tightly. Smooth out parchment and line pan with parchment, overlapping as needed to ensure it covers sides. (Because the parchment needs to be pleated and creased in some areas to fit in the pan, you won’t end up with clean, smooth outer edges to the cake; that’s okay.) Place pan on a rimmed baking sheet. 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 (mixture will be thick and pasty); set espresso mixture aside.
Step 2
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. (Alternatively, use a large bowl with a hand mixer on medium low-speed; you may need to beat a few extra minutes to dissolve the sugar.)
Step 3
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. Scrape down sides of bowl and continue to beat until batter is very smooth and silky, about 10 seconds more.
Step 4
Transfer half of batter to bowl with reserved espresso mixture (if espresso mixture is very lumpy, loosen with a few spoons of batter first before adding the rest); stir with rubber spatula until incorporated.
Step 5
Alternating between batters, scrape large dollops into prepared pan (eyeballing is fine). 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 (cake will collapse as it cools). Transfer to refrigerator and chill until cold, at least 4 hours.
Step 6
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 4 minutes. Spoon over chilled cheesecake, swirling as desired. Chill until topping is set, about 15 minutes.
Step 7
To serve, dust top of cheesecake with cocoa powder. Remove sides from pan and carefully peel away parchment paper from cheesecake. Slice into wedges.
Do Ahead: Cheesecake can be made 2 days ahead. Cover and chill.
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