Preheat oven to 400 degrees. Grease a rimmed half sheet pan.

Add the sugars, flour, baking soda, and salt to the bowl of a stand mixer fitted with the paddle attachment.

Add 1 cup of milk, peanut butter, and butter to a small sauce pan and bring to a boil, stirring often.

Remove from heat and let set for 5 minutes to cool. Add to the bowl with the flour and sugar.

Add the remaining 1/2 cup of milk, vanilla, and eggs to the mixer and turn to low speed. Mix until just combined.

Spread cake batter into prepared baking sheet and bake for 15 minutes. Cool completely.

To make the frosting, add the sugar, butter, and milk to a small sauce pan and stir well. Bring to a boil and boil for exactly 60 seconds.

Remove from the heat and stir in the peanut butter and chocolate chips until smooth and melted.

Pour warm frosting over the cooled cake and spread with a spatula. Frosting will harden as it cools.

Cut and serve once frosting has cooled and set.