**Prepare the crust**
Preheat your oven to 325°F (165°C). In a medium bowl, combine the graham cracker crumbs, sugar, and melted butter. Mix until the texture resembles wet sand. Press the mixture firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes, then let it cool while you prepare the filling.
**Make the filling**
In a large mixing bowl, beat the softened cream cheese until smooth and creamy, about 2–3 minutes. Add the granulated sugar and brown sugar, and mix until fluffy. Beat in the eggs one at a time, mixing just until incorporated. Add the vanilla extract, brewed espresso, and espresso powder. Mix until fully combined, then fold in the sour cream.
**Assemble and bake**
Pour the cheesecake filling over the cooled crust. Wrap the bottom of the springform pan with aluminum foil to prevent water from seeping in. Place the springform pan in a roasting pan and fill the roasting pan with hot water until it reaches halfway up the sides of the springform pan. Bake for 60–70 minutes, or until the edges are set and the center is slightly jiggly.
**Cool and chill**
Turn off the oven and leave the cheesecake inside with the door slightly open for 1 hour. Remove from the water bath and let it cool to room temperature. Cover and refrigerate for at least 4 hours, or overnight, to fully set.
**Add toppings and serve**
Dust the cheesecake with cocoa powder, sprinkle chocolate shavings, or decorate with chocolate-covered espresso beans before serving. Slice with a warm knife for clean cuts and enjoy chilled.