Preheat oven to 350° (175°C). Lightly grease an 8-inch square baking pan. Line with parchment paper (or foil), leaving a couple of inches of overhang on two sides. Grease parchment.
Place the butter and chocolate in a microwave-safe bowl. Microwave at half power in 30-second intervals until butter is melted and chocolate melts when stirred. Stir to combine. Transfer to a large mixing bowl and set aside to cool slightly.
Whisk together the flour, baking powder, and salt. Set aside.
Add the sugar to butter/chocolate mixture, and mix well. Add the eggs, one at a time, mixing well after each addition. Mix in the vanilla.
Place the peanut butter in a small microwave-safe bowl. Heat for 20-30 seconds, or until it can be easily stirred. Add to the chocolate mixture, and mix until combined.
Gradually add the flour mixture, mixing just until combined. Stir in about 3/4 of the pretzels.
Transfer the batter to the prepared pan and spread evenly. Place the remaining pretzels over the top of the batter, and press down gently into the batter.
Bake 40-45 minutes, or until a pick inserted into the center comes out with moist crumbs attached. Cool completely in the pan on wire rack.
Using overhanging parchment, lift the brownies from the pan onto a cutting board. Using a sharp knife, cut into bars.