Preheat your oven to 325 degrees F. Prepare a 9”x13” metal baking dish by spraying the bottom and sides with nonstick spray. You can also want to line the bottom and side with parchment paper and spray again. Set aside. NOTE: you can use a glass baking dish but the bars will take a few minutes longer to bake and the edges might not be as crunchy.
In a medium size mixing bowl, whisk together the flour, baking soda, and salt. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, or with a hand beater, beat the butter and peanut butter until smooth.
Add the brown sugar and granulated sugar and mix on medium-high speed for about a minute, making sure to scrape down the sides and bottom of the bowl as needed.
Add the vanilla and eggs and beat until well mixed.
Stir in the flour mixture on low speed and mix until no streaks of flour remain.
Fold in the oats.
Put the batter into the prepared pan. It will be a thick batter, similar to cookie dough, but a little stickier. Evenly press the batter into the pan and bake for 20 to 25 minutes.NOTE: you want it to be slightly underdone in the center - and don't worry if it sinks a little when cooling. That's meant to happen. Remove the pan from the oven and allow to cool completely before adding the buttercream.