Line an 8-inch or 9-inch square baking dish with parchment paper, leaving some overhang around the edges to make the bars easier to lift out later.
Add the butter and brown sugar to a large saucepan. Heat over medium heat, stirring until the butter melts and the brown sugar dissolves.
Stir in the vanilla extract, then add the rolled oats.
Reduce the heat to low and cook for 3–4 minutes, stirring frequently, until the oat mixture is thoroughly combined.
Transfer half of the oat mixture to the prepared baking dish. Spread it into an even layer and press it firmly into the bottom of the pan.
Place the chocolate chips and peanut butter in a microwave-safe bowl. Microwave in short intervals, stirring between each one, until completely melted and smooth.
Pour the chocolate-peanut butter mixture over the oat base, reserving about 1/4 cup for the topping. Spread the filling evenly.
Spoon the remaining oat mixture over the chocolate layer and gently press it into place.
Drizzle the reserved chocolate mixture over the top of the No Bake Chocolate Oatmeal Bars.
Refrigerate for 2–3 hours, or overnight, until firm.
Allow the bars to sit briefly at room temperature before slicing and serving.
Notes
For thinner bars, use a larger baking dish and adjust the chilling time as needed.