Melt the dark chocolate and butter together in a large heat-proof bowl and whisk until smooth.
Add the sugar, coffee powder, and vanilla extract, then whisk until well incorporated.
Crack in the eggs and whisk vigorously until the batter is smooth and combined.
Sift in the cocoa powder and baking powder, then gently fold until just combined.
Pour the batter into a 6-inch cake tin that has been lined with baking paper and lightly oiled.
Bake at 180°C for 25 minutes; the cake should still have a slight jiggle in the center.
Remove from the oven and allow the cake to cool completely in the tin to set its structure.
Once cooled, carefully remove from the tin and serve at room temperature.