Preheat oven to 325°F (163°C). Prepare a 9-inch springform pan with butter or non-stick spray. Bake the crust (graham cracker crumbs, sugar, and melted butter) for 10 minutes, then set aside to cool.
Beat cream cheese until smooth, then add granulated sugar and vanilla extract, beating until combined. Add eggs one at a time, mixing well after each addition.
Dissolve espresso powder in hot water. Add espresso mixture, coffee liqueur, sour cream, and heavy cream to the cream cheese mixture, mixing until smooth.
Pour the filling over the cooled crust. Tap the pan to release air bubbles. Bake for 55-65 minutes until edges are set but the center jiggles slightly.
Let the cheesecake cool in the oven for 1 hour, then cool completely at room temperature. Refrigerate for at least 4 hours before serving.
Remove from the pan, slice, and serve.
Notes
For the best flavor and texture, ensure all ingredients are at room temperature before starting, and avoid overmixing the batter.