Heat oven to 350°. Grease a 9" x 13" baking pan with butter and line with parchment paper; grease paper. Set pan aside.
Pour enough water into a 4-quart saucepan that it reaches a depth of 1". Bring to a boil; reduce heat to low. Combine butter and chocolate in a medium bowl; set bowl over saucepan. Cook, stirring, until melted and smooth, about 5 minutes. Remove from heat; set aside.
Whisk together eggs in a large bowl. Add sugar, brown sugar, vanilla, and salt; whisk to combine. Stir in chocolate mixture; fold in flour. Pour batter into prepared pan; spread evenly. Bake until a toothpick inserted into center comes out clean, 30–35 minutes. Let cool on a rack. Cut and serve.