Preheat: Preheat your oven to 350 degrees F (175 degrees C).
Creaming the Base: In a large bowl or stand mixer, cream the softened butter, sugar, and brown sugar until smooth and creamy.
Adding Flavor: Mix in the vanilla extract, eggs, water, and peanut butter until well combined.
Combining Dry Ingredients: Gradually add the old-fashioned quick oats, flour, baking soda, and salt. Mix until the dough is well combined and forms a cohesive mixture.
Baking the Base: Spread the dough evenly onto the baking sheet. Bake in the oven for 15 minutes or until the edges are lightly golden.
Letting it Set: Allow the bars to cool completely.
Preparing the Frosting: While the bars are cooling, use a hand mixer to blend the melted butter, milk, vanilla, cocoa powder, and powdered sugar until the frosting is smooth and creamy (around five minutes).
Adding the Finishing Touch: Once the bars have cooled, spread the chocolate buttercream frosting over the top.
Cut and Serve: Cut the bars into your desired sizes and shapes. Serve and enjoy these delectable Lunch Lady Peanut Butter Bars!