Preheat your oven to 375°F and grease an 8-inch round cake pan. Line the bottom with parchment paper and grease the paper.
Melt the chocolate and butter in a heatproof bowl over a pot of simmering water, stirring until smooth. Remove from heat.
Stir in the sugar, salt, and vanilla extract into the chocolate mixture.
Add the eggs one at a time, stirring well after each addition.
Sift the cocoa powder over the chocolate mixture and fold until just combined.
Pour the batter into the prepared pan and smooth the top with a spatula.
Bake for 25 minutes, until the cake has a thin crust on the top.
Cool the cake in the pan on a wire rack before inverting onto a plate. Remove the parchment paper.
Serve at room temperature or chilled, as preferred.