Preheat oven to 325°F (170°C). Line a baking sheet with parchment paper.
For cookie: Within the bowl of a stand mixer fitted with the paddle attachment, beat butter, peanut butter, and brown sugar at medium pace till gentle and creamy, about 2 minutes, stopping to scrape backside and sides of bowl. Add flour, peanuts, and salt; beat at low pace till simply mixed. Switch dough to ready pan; gently pat right into a 1⁄8-inch-thick circle.
Bake till golden brown, 20 to 25 minutes. Let cool fully. Depart oven on.
Break cooled cookie into bite-size items.
For cake: Clear bowl of stand mixer and paddle attachment. Utilizing the paddle attachment, beat butter, peanut butter, cream cheese, granulated sugar, and brown sugar at medium pace till gentle and fluffy, 5 to 7 minutes, stopping to scrape backside and sides of bowl and paddle. Add eggs, separately, beating effectively after every addition. Beat in vanilla.
In a small bowl, whisk collectively flour and salt. With mixer on low pace, add flour combination to butter combination in three additions alternately with milk, starting and ending with flour combination, beating simply till mixed after every addition.
Spray a 6-cup charlotte cake pan with baking spray with flour. Sprinkle 1⁄2 cup (about 40 grams) cookie crumbles round interior circle in backside of ready pan.
Gently fold 1½ cups (about 146 grams) cookie crumbles into batter. (Reserve remaining crumbles.) Fastidiously spoon batter into ready pan, smoothing with an offset spatula. Firmly faucet pan on a kitchen towel-lined counter a number of instances to settle batter.
Bake till a picket decide inserted in middle comes out clear, 55 minutes to 1 hour and 5 minutes, masking with foil midway via baking to forestall extra browning. Let cool in pan for quarter-hour. Invert cake onto a wire rack, and let cool fully.
For icing: In a big bowl, whisk collectively confectioners’ sugar, peanut butter, cream, and vanilla till clean and effectively mixed. Unfold onto cooled cake; sprinkle with remaining cookie crumbles. Retailer in hermetic container for as much as 3 days.
