Preheat your oven to 350°F (175°C). Grease your 9x13 inch baking pan or line it with parchment paper for easy removal.
In a medium saucepan, melt the butter and unsweetened chocolate over low heat, stirring constantly until smooth. Once melted, remove from heat and let it cool slightly.
In a large mixing bowl, combine the melted chocolate mixture with granulated sugar. Stir until well combined. Add the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract.
In the same bowl, sift together the all-purpose flour and salt. Gently fold the dry ingredients into the wet ingredients until just combined. Be careful not to overmix.
Gently fold in the peanut butter chips, distributing them evenly throughout the batter.
Pour the brownie batter into the prepared baking pan and spread it evenly. Bake in the preheated oven for about 25-30 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
Once baked, remove the brownies from the oven and allow them to cool completely in the pan on a wire rack.
In a mixing bowl, combine the softened butter, creamy peanut butter, and confectioners sugar. Add 3-4 tablespoons of milk and mix until smooth and creamy. Adjust the consistency by adding more milk if needed.
Spread the peanut butter frosting evenly over the cooled brownies.
In another bowl, mix together the softened butter, unsweetened cocoa powder, and confectioners sugar. Gradually add 1/4 cup of milk and the vanilla extract, whisking until the frosting is smooth and spreadable.
Spread the chocolate frosting over the peanut butter frosting layer, creating a beautiful two-toned effect.
Once the frosting has set, slice the brownies into squares and serve.