Preheat your oven to 350F (175C). Line a 9x9 inch baking pan with parchment paper and lightly grease the sides.
In a microwave-safe bowl, combine the butter and chocolate chips. Microwave in 30-second intervals, stirring between each, until fully melted and smooth. Let the mixture cool for 5 minutes.
Whisk the sugar, eggs, and vanilla extract into the melted chocolate mixture until well combined and glossy.
Add the flour, cocoa powder, and salt. Fold everything together with a spatula until just combined and no dry streaks remain. Do not overmix.
Pour half of the brownie batter into the prepared pan and spread it evenly. Arrange the peanut butter cups in an even layer across the batter, pressing them in gently. Pour the remaining batter over the top and smooth it out to cover the peanut butter cups completely.
Bake for 28 to 32 minutes, until the top is set and a toothpick inserted in the center comes out with a few moist crumbs. The key to fudgy brownies is pulling them out at the right moment, so avoid overbaking.
Let the brownies cool completely in the pan before slicing into squares. For the cleanest cuts, refrigerate for at least 1 hour first.