Preheat the oven to 350°F. Line a 9x13-inch baking pan with parchment paper, leaving overhang on the sides for easy removal.
In a large bowl, whisk together the melted butter, melted chocolate, and granulated sugar until smooth and glossy.
Add the eggs one at a time, whisking well after each addition. Stir in the vanilla extract.
Add the flour, cocoa powder, and salt. Fold gently until just combined. Do not overmix.
Spread the batter evenly into the prepared pan.
Bake for 28–32 minutes, or until a toothpick inserted near the center comes out with a few moist crumbs attached.
Allow the brownies to cool completely.
In a medium bowl, beat together the peanut butter and softened butter until smooth and creamy.
Add the powdered sugar, vanilla extract, and salt. Beat until fully combined.
Spread the peanut butter mixture evenly over the cooled brownies.
Refrigerate for 15–20 minutes to firm the peanut butter layer.
In a microwave-safe bowl, combine the chocolate chips and peanut butter.
Microwave in 30-second intervals, stirring between each interval, until melted and smooth.
Pour the chocolate mixture over the peanut butter layer and spread evenly.
Sprinkle with flaky sea salt if desired.
Refrigerate for about 1 hour, or until the chocolate topping is fully set.
Let the brownies sit at room temperature for 10 minutes before slicing into 24 squares.