For the peanut butter cookie dough: Whisk together 2 cups flour, 1/2 teaspoon baking soda and 1/2 teaspoon salt in a large bowl.
Beat 1 stick plus 2 tablespoons butter, 1/2 cup dark brown sugar and 1/2 cup granulated sugar together in a large bowl with an electric mixer until light and fluffy, about 4 minutes. Add 1 egg and beat until completely incorporated, scraping down the sides of the bowl as needed. Beat in the peanut butter and 1 teaspoon vanilla until creamy. Reduce the speed to medium and add the flour mixture, then beat until completely incorporated. Turn out the dough and form into a 3/4-inch-thick rectangle, then wrap tightly in plastic. Freeze until beginning to firm up, 30 minutes. (Do not over-chill or the dough will crack when rolled.)
Meanwhile, make the sugar cookie dough: Whisk together 2 cups flour, 1/2 teaspoon baking soda and 1/2 teaspoon salt in a large bowl.
Beat 2 sticks butter and 1 cup granulated sugar together in a large bowl on medium-high speed with an electric mixer until light and fluffy, about 4 minutes. Add 1 egg and 1 teaspoon vanilla and beat until completely incorporated, scraping down the sides of the bowl as needed. Reduce the speed to medium, add the flour mixture and beat until completely incorporated. Turn out the dough and form dough into a 3/4-inch-thick rectangle and wrap tightly in plastic. Freeze until beginning to firm up, 30 minutes. (Do not over chill or the dough will crack when rolled.)
Make the brownie batter: Whisk the cocoa together with the remaining 1/2 cup flour, 1/2 teaspoon baking soda and 1/4 teaspoon salt in a medium bowl. Melt the remaining 6 tablespoons butter and whisk with the remaining 3/4 cup dark brown sugar in another medium bowl until incorporated. Add the remaining 2 eggs and 1 teaspoon vanilla and whisk until smooth with no large lumps of sugar remaining. Fold the dry mixture into the wet mixture and stir vigorously for 15 seconds until the batter is very thick and smooth.
Generously flour a large piece of parchment paper and roll the peanut butter dough into a 16-by-12-inch rectangle. Repeat with the sugar cookie dough. Using the parchment to help you, lift the sugar cookie dough and flip it onto the peanut butter dough, parchment-side up, so that edges of both doughs are lined up. Brush off any excess flour and trim the edges to square off all sides. Evenly spread the brownie batter over the entire surface of the sugar cookie dough using an offset spatula. Position the dough so that one of the short sides is facing you. Working from the bottom edge closest to you and using the parchment to help you, roll the dough up tightly, peeling back the parchment as you roll and form a tight log. Keep the log covered in parchment and freeze until firm, about 30 minutes. Remove from the freezer and roll gently on the counter to create a more circular log. Freeze until solid, at least 5 hours and up to 24.
Position 2 oven racks in the upper and lower thirds of the oven and preheat to 375 degrees F. Line 2 baking sheets with parchment paper.
Slice half the frozen dough with a sharp knife into 1/2-inch slices (keep the remaining dough frozen until ready to bake) and place on the lined pans spaced 2 inches apart (about 6 per sheet). Bake, switching the positions of the cookie sheets halfway through, until the peanut butter cookie is golden brown but the sugar cookie is still blonde, 14 to 18 minutes. Let cool for 15 minutes on the baking sheets, then transfer to racks to cool completely.
Let the baking sheets cool completely, then slice the remaining frozen dough and repeat.
Store the cookies in a tightly sealed container at room temperature for up to 5 days.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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