Preheat the oven to 400 degrees F (200 degrees C). Butter a 9x13-inch baking pan.
Combine brown sugar, butter, corn syrup, 1/4 cup peanut butter, and vanilla extract in a bowl. Add oats gradually. Press bar mixture into the prepared pan.
Bake in the preheated oven until golden brown, 12 to 14 minutes. Let cool for 4 minutes.
Melt chocolate chips, butterscotch chips, and 1/3 cup peanut butter in a microwave-safe bowl in 15-second intervals, stirring after each melting until blended, 1 to 3 minutes. Spread over warm bars. Let cool before cutting, 2 to 3 hours.