In a small saucepan, combine the butter and brown sugar and warm the mixture, stirring often, until melted and smooth. Using a rubber spatula, scrape this mixture into a large bowl and let cool.
In a small bowl, whisk together the flour, baking powder, and salt.
Add the eggs and vanilla to the cooled butter mixture and mix with a large spoon until smooth.
Add the flour mixture and stir just until combined.
Pour the batter into the prepared pan.
Bake for 20-25 minutes or until a toothpick inserted in the centre comes out clean. Let cool completely.