Preheat oven to 350° F. Line an 9 inch springform baking pan with parchment paper.
In a 2-3 quart saucepan, melt the butter over low heat. Remove from heat and allow to cool to room temperature.
Mix in sugar and brown sugar. Stir in beaten eggs.
Mix in peanut butter and vanilla.
Mix in flour, baking soda and baking powder, just until fully incorporated and no flour is visible.
Stir in any mix-ins just until incorporated. Spread batter into prepared pan.
Bake for 50-55 minutes. The cookie cake is done when the edges are browned and a toothpick inserted in the middle comes out clean. Allow the cookie cake to cool completely in the pan. The middle will sink as it cools.
Frosting. In a bowl of an electric mixer (or bowl with a hand mixer), mix the cocoa powder, half the confectioner’s sugar and salt. Stir in the hot milk and the vanilla. Add the butter and rest of the confectioner’s sugar, beating until light and fluffy, approximately 2-3 minutes.
Assembly. Slide a metal spatula around the inside edge of the baking pan to loosen the blondie cake from the sides. Release the side portion of the springform pan. Using a spatula, lift the cookie cake onto a serving plate. Spread the frosting over the sunken part of the cookie cake.