Preheat the oven to 325 degrees F.
Place the butterscotch chips and the first 3 tablespoons of butter into a glass bowl and microwave in 30-second increments until melted. Stir every 30 seconds. This should take one minute to one and a half minutes. Add the vanilla and stir until smooth; let cool for 15 minutes.
Beat the second amount of measured butter (9 tablespoons) with the sugar and salt. Beat until the mixture is light and fluffy.
Add the cooled butterscotch mixture and continue to mix until combined. Add egg yolk then reduce to a lower speed to add the dry ingredients of flour and baking powder. A dough will come together and that is your signal to stop mixing.
Form dough into a log approximately 2 inches in diameter and 9-10 inches in length. Chill until firm (min 30-60minutes). Slice 1/4 inch thickness and place on parchment lined baking sheet approximately 1 inch apart.
Alternate method: Pinch off enough dough to make approximately one inch balls ( or use a 1-inch ice cream scoop to measure out dough). Place on a parchment lined baking tray approximately 2 inches apart.
Bake for 12-15 minutes or until the edges just start to brown. Cool on wire racks.