Preheat the oven to 350°F (175°C). Grease an 8-inch round cake pan and line the bottom with parchment paper.
Melt the chocolate and butter in a double boiler over low heat, stirring until smooth. Remove from heat and let cool slightly.
Whisk together the sugar, eggs, vanilla extract, and salt in a large mixing bowl until well combined.
Slowly add the melted chocolate mixture to the egg mixture, stirring continuously.
Sift in the cocoa powder and gently fold until fully incorporated.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 25-30 minutes, or until the center is set and a toothpick inserted comes out with a few moist crumbs.
Let the cake cool completely in the pan before frosting.
Prepare the Frosting:
Heat the heavy cream in a small saucepan over medium heat until warm but not boiling.
Pour the warm cream over the chopped chocolate in a heatproof bowl. Let sit for 1 minute, then whisk until smooth.
Stir in the powdered sugar and vanilla extract and whisk until the frosting is glossy.
Spread the frosting over the cooled cake with a spatula.
