Preheat the oven to 350°F. Line an 18x13-inch half sheet pan with parchment paper and set aside.

In a large bowl, or the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, granulated sugar, and brown sugar for 1-2 minutes or until light and fluffy.

Add 1½ cups peanut butter, eggs, and vanilla extract, mixing on low speed just until well combined.

In a separate bowl, stir together the all-purpose flour, old-fashioned oats, baking soda, and salt. Add the dry ingredients into the peanut butter mixture, mix on low just until all the ingredients are evenly distributed and no dry pockets of flour remain.

Transfer the peanut butter batter to the prepared sheet pan and press out into an even layer. The batter will be quite sticky. Use a separate piece of parchment paper, or lightly dampened hands (with cool water), to press the batter to all the edges of the pan without too much batter sticking to your hands.

Bake for 15 minutes or until the center no longer looks glossy and the edges are lightly golden. Do not overbake the peanut butter base or your bars will turn out dry and crumbly when cooled.

Remove the sheet pan from the oven. Add small dollops of the remaining 1 ½ cups peanut butter to the warm base. Allow the peanut butter to sit for 2-3 minutes or until starting to melt. Using a small offset spatula, gently spread the melted peanut butter into a thin even layer, leaving a ¼ to ½-inch border around the edges to make lifting and slicing easier once cooled.

Allow the peanut butter base to cool completely, and the melted peanut butter layer to fully firm, before preparing the chocolate frosting. This can take 1 to 1½ hours depending on the temperature in your kitchen.

In a large bowl, using a handheld mixer on medium speed, beat the unsalted butter for 1-2 minutes or until light, fluffy, and no lumps remain.

Add the powdered sugar, unsweetened dutch-processed cocoa powder, salt, vanilla extract, and 4 tablespoons whole milk to the bowl and mix on low speed just until all the powdered sugar is incorporated.

Increase the speed to medium-high and mix for another 1-2 minutes or until the frosting is light and smooth. You can add the additional 1 tablespoon whole milk if needed to lighten up the frosting to an easily spreadable consistency. The frosting will be slightly denser than if frosting a cake or cupcakes but it should spread easily when frosting the peanut butter base.

Once the peanut butter base has cooled completely, and the peanut butter layer has firmed, use a small offset spatula to carefully spread the frosting into a thin even layer over the peanut butter layer, leaving a ¼ to ½-inch border around the edges.

Allow the frosting to set for 20-30 minutes at room temperature to allow the frosting to dry slightly making slicing and stacking easier for serving.