Preheat oven to 350°F. Butter 8-inch square pan, then line with 2 fitted strips of overlapping parchment paper, leaving a 2-inch overhang on all sides.
In large microwave-safe bowl, melt butter and chocolate on high, stirring every 45 seconds, until melted and smooth, 2 to 3 minutes.Stir in sugar and salt until combined.
Whisk in eggs, 1 at a time, until smooth. Whisk in flour and vanilla until mixture is smooth and glossy. Scrape into prepared pan, smoothing top.
Bake until top is set and slightly shiny brownies should not spring back when pressed), 25 to 26 minutes. Let cool completely on rack; cut into squares.