In a saucepan, mix together the butter and brown sugar until completely combined and the sugar dissolves.
Add vanilla extract, 3 tbsp peanut butter, rolled oats, and a pinch of salt. Stir together and cook for a few minutes, stirring occasionally. Remove from heat.
Line an 8-inch square baking pan with parchment paper. Transfer 2/3 of the oatmeal mixture to this prepared pan. Spread evenly using a spatula or your hands. Set aside.
In a microwave or on the stove, melt together 1 cup of chocolate chips and 1/3 cup of peanut butter. Stir until incorporated and completely melted. You can reserve a few tablespoons of this chocolate mixture for topping. Pour over the oatmeal base. Spread evenly.
Top with reserved 1/3 of the oatmeal mixture and peanuts (optional). Let it cool to room temperature. Then, refrigerate until set.
Remove from the refrigerator. Let the chocolate oatmeal bars warm up to room temperature. Slice and drizzle with reserved chocolate/peanut mixture (if desired) and serve!