Preheat the oven to 350° and grease and line the base of a 10 inch springform pan with parchment paper. In the bowl of a stand mixer combine melted butter, peanut butter, light brown sugar, granulated sugar, vanilla extract and eggs. Mix on medium speed for 30 seconds until combined.
With the mixer on low add in the flour, corn starch, baking soda and salt. Mix on low until incorporated. Remove the bowl from the stand and fold in the chocolate and peanut butter chips with a spatula. Spread the cookie dough in the prepared pan and bake for 25-30 minutes or until the cookie is lightly browned and looks dry on the surface. Allow to cool completely before frosting.
For the frosting:
In the bowl of the stand mixer cream the butter, cocoa powder, powdered sugar and salt on medium speed until combined. Add in the milk, 1 tablespoon at a time, until smooth and creamy.
Add the frosting to a piping bag fitted with a tip and pipe a border of frosting around the edge of the cake. Top the frosting with sprinkles, slice and serve!