Preheat oven to 325°F (165°C). Grease a springform pan.
Mix crumbs, sugar, and melted butter. Press firmly into the bottom of the pan. Bake for 10 minutes and let cool.
Beat cream cheese until smooth. Add sugar and mix until creamy.
Add eggs one at a time, mixing just until combined.
Blend in sour cream, dissolved espresso, and vanilla extract.
Pour filling over crust and smooth the top.
Bake for 50–55 minutes, until edges are set and center slightly jiggles.
Cool completely, then refrigerate at least 4 hours before serving.