In a large bowl beat together the butter, brown sugar and white sugar until fluffy.
Add in the egg, egg yolk and vanilla extract.
Turn the mixer down to low speed and mix in the flour, baking soda and salt.
Turn off the mixer and stir in 1 cup butterscotch chips. You'll use the remaining ¼ cup later. **Don't mix all the butterscotch chips into the dough - otherwise the cookies can spread too thin.
Cover the bowl with plastic wrap and refrigerate the cookies for 2 hours or overnight.
Preheat the oven to 350F (180C) degrees and line cookie sheets with parchment paper or silicone baking mats.
Form the dough into balls with about 1-1.5 tablespoons of dough each. They'll be about the size of a golf ball or a little smaller. I like to use a cookie scoop for this. Place the balls 2 inches apart on the lined cookie sheets.
Bake 1 sheet at a time on the middle rack of the oven for 9-11 minutes, or until the tops look just set. Remove from the oven and place a few extra butterscotch chips on the top of each cookie (from the reserved ¼ cup).
Cool cookies on the cookie sheet for at least 10 minutes, then transfer to a wire rack to continue cooling.