PREP: Preheat oven to 350 degrees F. Generously grease or add parchment paper to a 17x12.25-inch jelly roll pan (Note 3). Set aside.
COOKIE BASE: In a bowl attached to a stand mixer (or use a large bowl with a hand mixer), cream together the softened butter (Note 4), white sugar, and brown sugar until smooth and creamy (the consistency of peanut butter). Add eggs; beat to combine. Add vanilla, baking soda, salt, and oats. Mix until just incorporated and then add in peanut butter. Mix until just incorporated. Finally, add in the flour and mix until just incorporated.
BAKE: Spread out dough in an even layer on the prepared sheet pan. Bake for 15-17 minutes and then remove. Be careful to not overbake the bars. We want a soft, chewy, and flavorful cookie base!
PEANUT BUTTER: Let cookie bars cool for 5 minutes then warm 1-1/2 cups peanut butter in the microwave for about 30-60 seconds or until it will drizzle nicely. Drizzle the peanut butter evenly on the cookie base and then, using a table knife or offset spatula, gently smooth peanut butter in an even layer. Then let the bars cool completely until the peanut butter has fully set up. (I pop the bars in the fridge/freezer for a little!)
FROSTING: Meanwhile, whip together the frosting. Add all the frosting ingredients to a large bowl (or a stand mixer) and beat until smooth and combined. Dollop scoops of frosting on top of bars and gently spread into an even layer.
CUT BARS: Cut into the bars with a hot sharp knife. Run the knife under hot water, dry it off, and then immediately cut the bars. Enjoy!
STORAGE: Cover leftover bars tightly and store at room temperature for up to 5-7 days. To freeze: Wrap each bar individually in plastic wrap and then store the wrapped bars in a large plastic bag or freezer-safe container. Freeze for up to 3 months. Thaw bars overnight in the fridge.