Brown the butter by placing it in a medium saucepan over medium low heat. Allow the butter to melt and foam. Stir occasionally but watch the butter carefully. As soon as it begins to turn an amber color stir until it is golden then remove it from the heat immediately. Cool for 10 minutes.
Preheat the oven to 350 degrees. Spray a 9 x 13 inch pan with cooking spray and set aside.
In a large bowl cream together the brown butter and brown sugar. Add in the eggs and vanilla and mix well.
Stir in the flour, baking powder, and salt (if using).
Pour the batter into the prepared pan. Bake for 35 minutes or until a toothpick inserted into the center comes out clean.