Line an 8x8-inch square pan with parchment paper. Set aside.

Set a large saucepan over medium heat and add the butter. When the butter is melted, add the brown sugar and vanilla extract. Stir until the sugar is dissolved.

Stir in the oats and cook for 3 minutes, stirring frequently.

Press half of the oatmeal mixture into the bottom of the lined pan. Transfer the remaining oatmeal mixture to a medium bowl and set aside. Wipe out the saucepan and return it to the stovetop.

Reduce to low heat, then add the chocolate chips and peanut butter to the saucepan. Stir frequently until the chocolate is melted.

Pour all of the melted chocolate mixture over the oatmeal mixture in the pan. Use a small rubber spatula or the back of a spoon to spread so that the bottom layer is covered completely.

Crumble the remaining oat mixture over the chocolate layer, pressing lightly so that it "sticks".

Cover and refrigerate for at least 2 hours or until set. Cut into small or large squares and serve cool or at room temperature.