Preheat oven to 350 degrees. Cream butter and sugars until light and fluffy. Melt butterscotch chips over a double boiler until melted. Add melted butterscotch chips and peanut butter to beaten butter and sugars. Beat in egg and vanilla.
Place flour, baking soda and salt in bowl; mix to combine. Add to wet ingredients until just combined then pour in butterscotch chips. Using a cookie scoop, scoop dough, roll in sugar then place onto baking sheet. Press tops with tines of fork if desired. Bake for 9-11 minutes or until cookies are cooked through. Remove and let cool for 5 minutes before transferring to cooling rack.