Preheat oven to 350 degrees. Spray a rimmed cookie sheet (standard half-sheet pan) lightly with non-stick spray and set aside.
Cream butter and sugars for 2-3 minutes, until light and 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 10-12 minutes. The center should be puffed and set, but still soft.
While crust is baking, prepare frosting. Whisk together powdered sugar, cocoa powder and salt. Add butter (make sure it’s soft!), boiling water (I ended up using 1/2 cup), and vanilla. Beat until smooth and glossy.
When cookie crust is done baking, pour frosting on top and spread. Let cool (or dig right in) and cut into squares to serve. Enjoy!