Preheat oven to 350°F (175°C). Grease or line a 9-inch square baking pan.
Place the butter and chocolate in a large microwave-safe bowl. Heat in the microwave at half power in 30-second increments until the butter has melted and the chocolate melts when stirred. Stir until smooth. Allow to cool slightly.
Whisk in the cocoa powder, followed by the sugar, and then the eggs and the vanilla. Add the flour and salt, and whisk until combined.
Stir in the peanut butter chips.
Transfer the batter to the prepared pan and spread evenly.
Bake 30 to 35 minutes, or until the edges are set and a pick inserted into the center comes out with a few moist crumbs attached.
Cool the brownies in the pan on a wire rack. Then cut into squares and serve.
Notes
*I usually have larger bags of peanut butter chips in my kitchen, but many brands are available in 10 ounce bags which contain about 1 & 2/3 cups. If that's what you have available, then that slightly lesser quantity will be just fine.
Store in an airtight container at room temperature up to 3 days or in the freezer up to 3 months.