In a microwave-safe bowl, melt the bittersweet chocolate and unsalted butter together in 30-second intervals, stirring after each interval until smooth (about 1 minute and 15 seconds in total). Let it cool slightly.

In the bowl of a stand mixer fitted with the whisk attachment (or using a hand whisk), whisk the granulated sugar, eggs, salt, and vanilla on high speed until pale and creamy, about 3 to 4 minutes.

Add the melted chocolate and butter mixture to the sugar and eggs mixture, mixing on low speed until combined.

Sift together the unsweetened cocoa powder, all-purpose flour, baking powder, and instant espresso powder. Add these dry ingredients to the wet ingredients, mixing on low speed until fully combined. Using a rubber spatula, fold the mixture by hand to ensure there are no lumps at the sides and bottom of the bowl. Reserve about 1 cup of the batter; set aside.

Pour the remaining brownie batter into the prepared baking pan, spreading it evenly.

Pour the cheesecake mixture over the brownie batter in the baking pan, spreading it evenly.

Add 1 tablespoon of hot water (or as needed to make the batter spreadable) to the reserved brownie mixture and stir until combined. Drop spoonfuls of the brownie batter over the cheesecake layer. Use a skewer or a butter knife to gently swirl the brownie batter and cheesecake mixture together to create a marbled effect.

Bake in the preheated oven for 1 hour or until a toothpick inserted into the center comes out with only a few moist crumbs.

Let the Cheesecake Brownies cool completely in the pan before cutting them into squares.