Preheat your oven to 375°F (190°C). Grease an 8-inch round cake pan and line the bottom with parchment paper.
Melt the butter and chocolate together in a heatproof bowl set over a pot of simmering water, stirring until smooth. Remove from heat and let cool slightly.
In a large mixing bowl, whisk together the sugar, eggs, vanilla extract, and salt until well combined.
Gradually add the melted chocolate mixture to the egg mixture, whisking constantly until smooth and well combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 25 minutes, or until the top is set and a toothpick inserted into the center comes out with a few moist crumbs.
Let the cake cool in the pan on a wire rack for 10 minutes, then remove from the pan and let cool completely on the wire rack.