Place the brown sugar and butter in a sauce pan over medium heat until sugar is melted. Stir so it doesn't burn.
Remove from he heat and let the mixture cool for 5 minutes.
Using an electric mixer, whisk together the eggs and the brown sugar/butter mixture and the vanilla.
Whisk in the flour, baking powder and salt and whisk until combined.
Prepare a 9 x 13 rimmed baking pan with cooking spray or rub butter on the bottom. Pour the batter into the pan.
Put the cake in a 375 degree preheated oven and bake for about 20 minutes. The cake will be a pretty golden brown. Do not over bake or you will have a dry cake!