Preheat your oven to 325°F (170°C). Prepare a baking sheet by lining it with parchment paper. This will prevent sticking and make cleanup a breeze.
For the cookie part, in the bowl of a stand mixer fitted with the paddle attachment, combine unsalted butter, creamy peanut butter, and light brown sugar. Beat on medium speed until it's light and creamy, which should take about 2 minutes. Don't forget to stop and scrape down the sides of the bowl to ensure everything is mixed well.
Next, gradually add the all-purpose flour, chopped peanuts, and kosher salt to the mixture. Beat at low speed until everything is just combined. You want to avoid overmixing, as this can make the cookie tough.
Transfer your dough to the prepared baking pan and gently pat it into a circle that’s about 1/8-inch thick. Place it in the oven and bake until golden brown, approximately 20 to 25 minutes. Once it’s done, let it cool completely before breaking it into bite-size pieces.
For the cake, clean the bowl of your stand mixer. Using the paddle attachment again, beat together softened unsalted butter, creamy peanut butter, full-fat cream cheese, granulated sugar, and light brown sugar on medium speed until the mixture is light and fluffy, which should take about 5 to 7 minutes. Make sure to scrape down the bottom and sides of the bowl throughout this process.
Incorporate the large eggs one at a time, mixing well after each addition. Follow this by adding the vanilla extract and beating until it’s fully mixed in.
In a separate small bowl, whisk together the all-purpose flour and kosher salt. With the mixer on low speed, add the flour mixture to the butter mixture in three parts, alternating with the whole milk. Start and end with the flour mixture, ensuring everything is just combined after each addition.
Spray a 6-cup charlotte cake pan with baking spray containing flour. Sprinkle about 1/2 cup of cookie crumbles around the inner circle at the bottom of the prepared pan. This layer will add a wonderful crunch to the cake.
Gently fold in 1 and 1/2 cups of the cookie crumbles into the cake batter, reserving the remaining crumbles for later. Carefully spoon the batter into the prepared pan, smoothing it down with an offset spatula. Give the pan a few firm taps on the counter to help settle the batter evenly.
Bake the cake until a wooden pick inserted in the center comes out clean. This can take anywhere from 55 minutes to 1 hour and 5 minutes. Cover the cake with foil halfway through baking to prevent it from browning too much. Once done, let it cool in the pan for about 15 minutes before carefully inverting the cake onto a wire rack to cool completely.
Now for the icing! In a large bowl, whisk together the confectioners’ sugar, creamy peanut butter, heavy whipping cream, and vanilla extract until the mixture is smooth and well combined.
Spread the icing over the cooled cake and sprinkle the remaining cookie crumbles on top for an extra crunch. Store any leftovers in an airtight container for up to 3 days.