Preheat oven to 350 degrees. Spray a rimmed cookie sheet (standard half-sheet pan) lightly with non-stick spray, or line with parchment paper, and set aside.
Cream butter and sugars for 3-4 minutes, until creamy and slightly fluffy. Add peanut butter and vanilla and beat until combined. Add eggs, one at a time and beat between each addition. Combine flour, baking soda, and salt and add mixture to dough. Beat to combine. Add oats and mix until incorporated.
Press dough into prepared pan into a flat layer. Bake for about 20-30 minutes, until puffed and set, but not browned on the edges. The center should be puffed and set, but still soft. The edges of the cookie bars should be puffed and kind of cracked like a baked cookie looks.
Optional Step: Some people like to drizzle on a layer of melted peanut butter onto the warm bars so there's a layer of pb under the icing. If you'd like to do that step, I just microwave 3/4-1 cup of pb until it's melted and smooth and can easily be drizzled over the top of the warm bars. You'll want to spread it gently so you don't tear your cookie layer. It's deliciously indulgent with or without this extra pb layer!
When cookies are just about done, prepare frosting. Whisk together powdered sugar, cocoa powder and salt. Add butter (make sure it’s really soft, you can microwave it if you need to- even melted is ok!), boiling water, and vanilla. Beat until smooth and glossy.
When cookie crust is done baking, pour warm frosting over the top and spread into an even layer. Let bars cool before cutting in.