Line two baking sheets with parchment and set aside.
Combine butter, brown sugar, granulated sugar, and milk in a medium saucepan.
Warm over medium heat, stirring until melted. Bring to a steady boil and cook 1 minute.
Remove from heat. Stir in peanut butter and butterscotch chips until completely smooth.
Mix in vanilla, cinnamon, and salt.
Fold in oats until evenly coated and thick.
Scoop heaping tablespoons onto the lined sheets and gently flatten.
Let set at room temperature 20–30 minutes, or chill 15 minutes, until firm.