Preheat oven to 350°F. Grease a 9-inch springform pan.
To make the shortbread base, combine flour, butter, sugar, and salt until crumbly. Press mixture into the bottom of the prepared pan. Bake for 20-25 minutes until lightly golden. Remove from the oven and let cool.
Reduce oven temperature to 300°F.
To make the vanilla filling, beat cream cheese, sugar, and vanilla extract until smooth. Add eggs, one at a time, and beat until just combined. Pour mixture into the cooled shortbread crust.
Bake for 45-50 minutes until set. Remove from oven and let cool.
To make the espresso & chocolate topping, heat heavy cream in a small saucepan over low heat until warm. Add chopped chocolate and espresso powder, whisking until smooth.
Spread espresso & chocolate topping over cooled cheesecake.
Chill cheesecake in the refrigerator for at least 4 hours or overnight before serving.