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.
Whisk in the sugar, then add the eggs one at a time, whisking well after each addition. Stir in the vanilla and salt.
Pour the batter into the prepared 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 rack.