Preheat the oven to 350 degrees
Butter and flour a 13x9x2 inch baking pan; do this by wiping the entire inside of the pan with butter, then sprinkle in enough flour to coat all of the butter by swirling it around; flip the pan over the sink, and lightly tap it to remove excess flour
Place the butter and chocolate into a large, heatproof bowl over a pan with simmering water, making sure the water isn’t high enough to touch the bowl; this is called a double boiler; you can also melt the chocolate and the butter in the microwave, but be careful not to overcook and/or burn it
Once melted together, set aside to cool
Combine the flour, baking powder, and salt into a bowl, and whisk together to combine
Once the butter and chocolate has cooled, whisk in the sugar
Then, whisk in the eggs one at a time, making sure each one is well incorporated
Whisk in the vanilla
Pour the flour mixture into the chocolate mixture in small increments, whisking each time
Mix until just combined; I like to switch to a spatula at this point
Stir in the chocolate chips and peanut butter chips until evenly mixed
Pour the brownie batter into the prepared baking pan; use a spatula, or knife, to evenly distribute the batter around the pan
Bake at 350 degrees for 25-30 minutes, or until a toothpick comes out clean; it is ok to under-bake these slightly; usually you can tell they are done if the middle is set