Preheat the oven to 180°C (360°F). Grease a 9-inch cake pan and line the bottom with parchment paper; place a rack in the middle of the oven.
In a large bowl, beat the 4 room-temperature eggs with 180 g sugar and 1 teaspoon vanilla extract on high speed until the mixture is pale, light, and frothy.
With the mixer running, slowly drizzle in 155 ml light olive or sunflower oil in a steady stream until fully incorporated, then whisk in 100 ml room-temperature espresso.
Sift together 300 g all-purpose flour and 1 tablespoon baking powder over the batter using a sieve; add a pinch of the 1/8 teaspoon sea salt and the 80 g dark chocolate chips, then fold gently with a whisk or spatula until just combined—do not overmix.
Pour the batter into the prepared pan and bake for about 40 minutes. If the top is browning too quickly, loosely cover with foil for the last 10 minutes. Test doneness with a toothpick—if it comes out clean, the cake is done.
Remove the cake from the oven and let it cool in the pan briefly, then remove from the pan and allow to cool completely on a rack.
For the mascarpone coffee cream, beat 250 g mascarpone with 3 tablespoons powdered sugar and 30 ml espresso until smooth; chill until ready to use.
Dust the cooled cake with powdered sugar or spread the mascarpone coffee cream on top before serving at room temperature.