Line a 9×9-inch square pan with parchment paper, leaving an overhang for easy removal.

In a medium saucepan over medium heat, melt the butter and brown sugar together, stirring constantly. Once bubbling, cook 1 minute more to dissolve the sugar crystals. Remove from heat.

Stir in vanilla, salt, and oats until fully coated. Press this oat mixture firmly into the prepared pan to form the base layer. Chill for 15 minutes in the fridge.

Meanwhile, combine peanut butter and chocolate chips in a microwave-safe bowl. Heat in 30-second bursts, stirring after each, until smooth and glossy.

Pour the chocolate-peanut butter mixture over the chilled oat layer, spreading evenly with a spatula.

Refrigerate for at least 2 hours—or until firm—before lifting out and cutting into 32 bars.