In a mixing bowl, whisk together flour, salt and baking soda, then whisk in oatmeal (chopped in blender or food processor) and set aside.
In the bowl of an electric stand mixer fitted with the paddle attachment, whip together butter, light brown sugar and granulated sugar on medium-high speed until pale and fluffy, about 3 - 4 minutes. Blend in 3/4 cup of peanut butter. Stir in eggs one at a time, mixing after each addition until combined. Mix in vanilla.
With mixer set on low speed. slowly added in dry ingredients and mix until combined. Spread mixture into an even layer into a 15 by 11 inch rimmed cookie sheet (it will be fairly thin once spread)
Bake in preheated oven for 13 - 15 minutes, until lightly golden. Remove from oven and allow to cool for 5 minutes, then dollop remaining 3/4 cup of peanut butter by spoonfuls over peanut bars. Allow dolloped peanut butter to rest about 1 minute then carefully spread peanut butter into an even layer over the top.
Prepare chocolate frosting according to directions listed and spread over peanut butter layer. Allow to cool before cutting into squares. store in a single layer in an airtight container at room temperature.
Melt butter in a medium saucepan over medium heat. Whisk in cocoa powder, then whisk in milk and bring just to a boil. Once mixture reaches a boil, remove from heat and stir in vanilla extract. Add in powdered sugar and mix until well blended. Immediately pour frosting over peanut butter layer and spread into an even layer (frosting sets quickly).