Preheat oven to 325 degrees. Line a 9x9 pan with parchment paper so that the paper is coming up over the sides.
Melt the butter, then allow it to cool so that it is no longer hot, but is still liquid. I usually melt the butter first, then place it in the freezer while I'm working on everything else.
Add the eggs and sugar to a stand mixer fitted with paddle attachment. Beat until the mixture is light yellow and thick, about 5-7 minutes.
Mix in the vanilla until just combined.
In a medium sized bowl, whisk together the flour, cocoa powder, salt, and baking powder.
On low speed, slowly mix flour mixture into egg mixture until just combined.
Then, still on low speed, slowly pour in cooled butter until just combined.
Spread evenly in prepared baking pan.
Bake for 30-32 minutes, or until toothpick inserted into center of pan comes out with just a few crumbs. Do not over bake.
Allow to cool in pan for 2 minutes, then use parchment paper to lift brownies out of pan and let cool on rack.