Prepare an 8×8-inch baking pan by lining it with parchment paper or foil. If using foil, lightly grease it. Set the pan aside.
In a microwave or using the double boiler method on the stovetop, melt the chocolate chips and peanut butter together until smooth. Set this mixture aside.
In a large saucepan over medium heat, melt the butter and brown sugar together, stirring until the sugar is dissolved.
Reduce the heat to low, then stir in the vanilla extract (if using). Add the quick oats and continue to cook, stirring constantly for 2-3 minutes, until the oats are well-coated.
Firmly press half of the oatmeal mixture into the prepared baking pan, creating an even layer.
Spread about three-quarters of the melted chocolate peanut butter mixture over the oatmeal layer, smoothing it gently to cover without disturbing the base.
Evenly distribute the remaining oatmeal mixture over the chocolate layer and press it down lightly to ensure it sticks together.
Drizzle the remaining chocolate peanut butter mixture over the top of the bars.
Refrigerate the bars for 2-3 hours or until the chocolate has completely set. Once firm, slice into bars and enjoy!