Preheat the oven to 350°F with a rack in the middle position.

Place the pretzel crumbs in a medium bowl. Pour the melted butter over them and mix with a spoon or rubber spatula until they are coated evenly and clump readily when pressed together.

Spoon three quarters of the mixture into a 9-inch pie plate and, using your fingers, press the mixture up the side of the plate until you have a 1/4-inch thick shell all the way around. Spoon the rest of the mixture into the center of the plate and press it to form the bottom of the shell, making sure the bottom and sides are joined.

Bake until the shell is lightly browned, 5 to 7 minutes. Remove it from the oven and let it cool on a rack, then transfer it to the refrigerator and chill for at least 30 minutes before filling.

Fill a medium saucepan with water, leaving a space of 2 to 3 inches at the top, and bring to a boil over medium-high heat.

Place the butter, chocolate, and 1/4 cup of the peanut butter in a large heatproof bowl (it would be big enough to sit on top of the saucepan and heat, stirring occasionally, until the butter, chocolate, and peanut butter have melted. Remove the bowl from the heat and whisk in the cocoa powder until smooth. Set the bowl aside to cool.

Place the remaining 1/4 cup peanut butter in a small saucepan over low heat and cook, stirring occasionally, until it's thinner and almost runny, 5 to 7 minutes. Remove from the heat and set aside.

Whisk together the eggs, sugar, and vanilla in a large bowl. Slowly pour the cooled chocolate mixture into the egg mixture and whisk briskly until smooth.

Stir together the flour, baking powder, and salt in a small bowl. Add to the brownie and stir until smooth.

Pour the brownie batter into the pretzel crust, filling it to just below the very top. Spoon three or four small dollops of the melted peanut butter on top of the brownie batter and gently swirl it into the batter with a table knife or toothpick.

Bake until a knife inserted 2 inches from the edge of the crust comes out clean, 35 to 40 minutes. Let cool before serving.