In a medium mixing bowl, combine the soft butter, peanut butter, demerara sugar, and granulated sugar. Use a whisk to mix until smooth and creamy, about 1 minute. Add the egg and whisk until fully incorporated. Stir in the flour with a rubber spatula until a cohesive dough forms. Do not overmix. Set the dough aside at room temperature.

Place the butter and dark chocolate in a heatproof bowl set over a saucepan of barely simmering water (or use a microwave-safe bowl and microwave in 30-second intervals), and heat until melted. Stir until smooth, then set aside to cool slightly.

In the bowl of a stand mixer fitted with the whisk attachment (or using a hand mixer), beat the eggs and salt until foamy. Slowly add the demerara sugar and granulated sugar, and continue beating until the mixture becomes thick, pale, and airy, about 4 to 5 minutes.

Using a spatula, gently fold the cooled chocolate mixture into the egg mixture in three additions. Sift in the cocoa powder and flour, and fold just until the batter is smooth and uniform. Avoid overmixing.

Preheat the oven to 355°F (180°C). Line or grease a 28 cm (11-inch) round cake pan or a 9 x 13-inch/23 x 33 cm rectangular baking dish.

Press half of the peanut butter cookie dough into the base of the prepared pan to form an even layer. Pour the brownie batter on top and smooth the surface with an offset spatula. Dot with small spoonfuls of peanut butter, scatter the remaining cookie dough in small chunks, and sprinkle with roasted peanuts.

Bake for 35 minutes, or until a toothpick inserted into the center comes out with moist crumbs. Let the brownies cool completely in the pan at room temperature. Once cool, slice into squares and serve.