Preheat oven to 350°F.
Grease a 9x13 inch pan with butter and set aside.
In a large microwave safe glass bowl, melt the butter on high for 30 seconds (or until butter is almost completely melted), covering the bowl with a paper towel.
Using a wooden spoon or sturdy spatula, mix in the brown sugar and stir until completely mixed.
Add the baking powder, salt and vanilla and mix well.
Gradually add the flour and mix well- the batter will be stiff.
Whisk the eggs well in a small bowl, and then add to the batter, mixing well one last time.
Spread the batter in the prepared pan (a spatula works well for this) and bake until golden around the edges and the center is still soft, about 30 minutes.
DO NOT OVERBAKE!
Let cool completely before cutting into squares.