Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius) and grease a 9x9 inch baking pan with butter or parchment paper.
In a primary mixing bowl, combine 1/2 cup melted butter with 1 cup granulated sugar. Whisk in 2 eggs and 1 teaspoon vanilla until the emulsion is smooth.
Sift 1/3 cup cocoa powder, 1/2 cup flour, and 1/4 teaspoon salt into the wet mixture. Fold until just combined and spread evenly into the prepared pan.
In a secondary bowl, cream 1/4 cup softened butter and 1/2 cup peanut butter with 1/4 cup granulated sugar and 1/4 cup brown sugar until aerated.
Incorporate 1 egg and 1/2 teaspoon vanilla into the peanut butter mixture.
Add 3/4 cup flour, 1/2 teaspoon baking soda, and 1/4 teaspoon salt, mixing until a cohesive dough forms.
Distribute the peanut butter cookie dough in rounded tablespoon portions across the surface of the brownie batter.
Bake for 30 to 35 minutes or until the cookie portions are golden and a tester inserted into the brownie layer returns with minimal moist crumbs.
Allow the pan to cool completely on a wire rack to ensure the crumb structure sets before slicing into 16 squares.