Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch baking dish.

Combine dark chocolate, sugar, butter, and salt in top of a double boiler over simmering water; heat, stirring frequently and scraping down the sides with a rubber spatula, until melted and smooth, about 5 minutes. Remove from heat and mix in eggs until well blended. Pour batter into the prepared baking dish.

Bake in the preheated oven until edges pull away from the sides of the baking dish, about 35 minutes.