In a medium bowl, whisk together flour, baking soda and salt. Set aside.
In the large bowl of a stand mixer, cream together butter, brown sugar and granulated sugar until light and creamy, about 2 minutes.
With the mixer on low speed, add the eggs, one at a time, mixing completely after each addition. Mix in the vanilla extract.
Gradually add the flour mixture, just until combined (do not over-mix). Stir in the butterscotch morsels.
Cover the dough and chill in the refrigerator for about 1 hour.
Preheat oven to 375°F. Line baking sheets with parchment or silicone mats.
Use a 1 ½-tablespoon cookie dough scoop to drop the dough balls two-inches apart on the prepared baking sheets. Add a few extra butterscotch chips to the top of each dough ball for garnish, if desired. Place the baking sheets back in the refrigerator or in the freezer for about 10 minutes to chill again.
Bake for 9-11 minutes, or just until lightly browned around the edges. The centers will still be soft. Let cool on the baking sheet for 5-10 minutes, then transfer to a wire rack to cool completely.