Brown the butter and let it cool for 2 minutes.
Add the warm brown butter to a large bowl. Whisk in the brown sugar, and then whisk in the egg and vanilla.
Stir in the flour and salt.
Transfer the batter to a prepared baking pan and spread it out evenly.
Bake until the blondies are golden along the outside and puffed, but still look a touch gooey in the center, about 20 to 23 minutes.