For the cookies: Whisk together the flour, cocoa powder, baking soda and salt in a large bowl. Beat the butter and brown sugar with an electric mixer on medium-high speed in a second large bowl until light and fluffy, about 6 minutes. Add the eggs to the butter mixture, one at a time, beating after each addition to incorporate; beat in the vanilla. Reduce the speed to medium, add the flour mixture, and beat until just incorporated. Fold in the chocolate chips by hand.
Roll the dough into 6 balls (about 1 1/2 cups each). Divide 4 of the balls between 2 rimmed baking sheets (2 balls per sheet). Flatten them into 6-inch circles using your hands; make sure the circles are 2 inches apart. Bake until just set, 12 to 14 minutes. Let cool on the baking sheet for 10 minutes, then transfer to a rack to cool completely. Repeat with the remaining 2 balls of dough.
For the frosting: Meanwhile, beat the butter and peanut butter with an electric mixer on medium speed in a large bowl until light and fluffy. Slowly add the confectioners' sugar about 1/2 cup at a time, beating between additions, until incorporated.
Assemble the cake: Place a cookie on a cake stand or serving plate and spread the top with some frosting. Top with another cookie and more frosting; repeat with the remaining cookies and frosting, making sure the frosting on the top layer is spread smooth.
For the ganache: Put the chocolate in a medium bowl. Bring the cream and butter to a boil in a small saucepan over medium heat. Pour over the chocolate and let stand for 5 minutes; stir until melted and smooth.
Pour the ganache over the top of the cake, smoothing the top with a small offset spatula and letting it drip over the sides. Decorate the rim of the cake with the peanuts. Let stand at room temperature until the chocolate hardens, about 10 minutes.
When measuring flour, we spoon 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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