Preheat the oven to 350 degrees F. Line a 9x13 baking pan with parchment paper.
Mix together the dry ingredients in a large mixing bowl - flour, old-fashioned oats, baking soda, salt, In the bowl of a stand mixer fitted with the paddle attachment, combine room temperature salted butter, brown sugar, and sugar.
Mix on medium speed for 3 minutes, until fluffy and lighter in color. Then add creamy peanut butter and vanilla extract and continue to mix until combined. Add eggs one at a time. Scrape down the sides of the bowl as needed. Add the oatmeal mixture to the stand mixer and mix until just combined. Batter should be thick.
Add batter to the baking pan and mash to make flatten to make an even layer. Bake peanut butter oatmeal bars for 30-35 minutes, until the center is set. Allow the bars to cool completely.
Make the chocolate layer. Melt chocolate chips in the microwave in a microwave-safe bowl for 30 seconds and then in 15 second increments until the chocolate is fully melted.
In a separate bowl, melt remaining peanut butter. Once the baked bars have cooled completely, pour melted chocolate on top of the bars. Drizzle the melted peanut butter on top and use a toothpick to swirl the peanut butter through the chocolate. Refrigerate or 30 minutes.
Add flaky salt on top (optional).