Preheat the oven to 350°F. Spray an 11x15 baking dish with cooking spray, set aside.
In a medium-sized bowl, stir together the oats, flour, salt, and baking soda, set aside.
In the body of a stand mixer with the paddle attachment, cream together the butter, brown sugar, and granulated sugar for 2 minutes.
Add ¾ cup of the peanut butter, the eggs, and vanilla, mix until combined. Scrape down the sides as needed. Add the dry ingredients and mix until just combined.
Press the dough into the prepared baking dish. Bake for 15-18 minutes until a toothpick inserted into the center comes out clean.
Place small dollops of the remaining 1 cup peanut butter on top. Wait 10 minutes to warm the peanut butter and carefully spread the peanut butter all over. Let cool completely.
While the bars are cooling, make the frosting. Place the powdered sugar, cocoa powder, and salt in a medium-sized bowl and stir to combine.
In a large bowl with an electric hand mixer, whip the butter until smooth. Start adding the powdered sugar mixture a little at a time until fully incorporated. Add the vanilla and 3 tablespoons of the milk, stir it in. Place the mixer on medium-high and whip the frosting for 3 minutes until light and fluffy. If it seems a little too thick to spread, add an additional 1 tablespoon of milk.
Once the bars are cool, spread the frosting on top. Let them sit for 30 minutes to give the frosting time to crust, or cut and serve immediately.