Preheat the oven to 350°F (175°C). Grease and flour an 8-inch cake pan.
In a bowl, whisk flour, cocoa powder, baking powder, and salt. Set aside.
In another bowl, beat eggs and sugar until light and fluffy. Stir in melted butter.
Gradually add dry ingredients and brewed espresso. Mix until smooth.
Pour batter into the prepared pan and bake for 30 minutes. Let the cake cool completely.
While the cake cools, prepare the mascarpone cream by whipping heavy cream, powdered sugar, and vanilla until soft peaks form.
Fold in mascarpone cheese until smooth and creamy.
For the chocolate ganache, heat heavy cream until simmering. Pour over chopped dark chocolate and stir until melted.
Once the cake has cooled, slice it into two layers. Soak each layer with espresso and coffee liqueur.
Spread a layer of mascarpone cream on the bottom layer. Place the top layer, then cover with more mascarpone.
Pour the ganache over the top, spreading it evenly. Refrigerate for at least 1 hour.