Preheat oven to 350°F (175°C) and line a 9-inch springform pan with parchment paper.

Melt 3/4 cup unsalted butter in a heat-safe bowl over simmering water, then whisk in sugars until smooth.

Add eggs and vanilla, mixing gently until fully incorporated.

Sift together flour, cocoa powder, and salt, then fold into the wet mixture until just combined.

Pour batter into the prepared pan and bake for 20-25 minutes, until a toothpick comes out with moist crumbs.

Let the brownie layer cool completely before preparing the cheesecake layer.

Wrap the cooled springform pan in aluminum foil for a water bath.

Beat cream cheese until smooth, then mix in sugar and cornstarch.

Dissolve coffee granules in hot water and add to the mixture with sour cream and heavy cream; blend until smooth.

Incorporate eggs one at a time on low speed, then pour over the cooled brownie base.

Place the springform pan in a larger dish, add boiling water, and bake at 300°F (150°C) for about 1 hour and 15 minutes.

Turn off the oven and let cheesecake cool inside for 30 minutes, then cool to room temperature.

Heat 1 cup heavy cream until simmering, stir in chocolate and coffee granules until smooth.

Pour ganache over cooled cheesecake and refrigerate for at least 8 hours.

Whip heavy cream with coffee granules and powdered sugar until stiff peaks form, then pipe onto cheesecake.

Garnish with chocolate curls or coffee beans before serving.