In a medium-sized pot or saucepan, over medium-low heat, melt the butter with the sugar until the sugar dissolves.
Mix in 3 tbsp of peanut butter, vanilla extract, oats, and a pinch of salt. Cook for 2-3 minutes until everything is well combined. Set aside.
Use parchment paper to line the bottom and sides of an 8-inch square baking pan and spoon ⅔ of the oatmeal mixture into the pan. Using a spatula or your hands, spread it evenly over the bottom of the pan.
Meat the chocolate chips with ⅓ cup of peanut butter in the microwave until smooth (start with 30 seconds and add 15 seconds at a time mixing before each time), and spread this mixture evenly over the oats.
Sprinkle the reserved ⅓ cup of oatmeal mixture and chopped peanuts on top.
Let cool completely, and refrigerate until set. Cut into bars and serve.