Preheat oven to 350°F. Grease an 9"x9" baking pan or line with parchment paper.
In a large mixing bowl, with an electric mixer or whisk, blend together melted butter and peanut butter until smooth.
Add granulated sugar and brown sugar, and mix until well combined.
Beat in eggs and vanilla extract.
Add flour, baking powder, and salt to the wet mixture. Mix until just combined.
Gently fold in the peanut butter chips until evenly distributed throughout the batter.
Pour the batter into the prepared baking pan, spreading it out evenly.
Bake 35-40 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Allow the brownies to cool in the pan before cutting into squares.