In a large bowl, cream together butter and sugars. Mix in vanilla and egg until smooth.
In a medium bowl whisk together flour, butterscotch pudding mix, and baking powder. Add dry mixture to wet ingredients and mix until combined. Stir in butterscotch chips. Cover and chill 1 hour.
Preheat oven to 350. Scoop about 2 tablespoons of dough and roll into balls. Place on lightly greased baking sheet at least 2 inches apart for spreading.
Bake 10-12 minutes. Immediately after removing from the oven, sprinkle cookies with coarse sea salt. Allow to cool completely on baking sheet. store in airtight container at room temperature.
Notes
If you find that the dough is too crumbly and doesn't quite come together after being mixed, add one additional egg to bring the dough together.