Use chilled butter so it won’t melt when you add the melted chips in step 2. If the chilled dough begins to split as you slice it, soften it on the counter for 10 minutes. Prep-time includes chill time.
Microwave 1/2 cup butterscotch chips and 3 tablespoons butter in bowl until melted, about 1 minute, stirring halfway through. Whisk in vanilla until mixture is smooth. Let it cool for 10 minutes.
In bowl whisk flour and backing powder. Set aside.
Cream remaining butter and brown sugar with your stand mixer on medium high speed until pale and fluffy. About 3 minutes. Scrape the bowl down during this time. Add cooled butterscotch mixture and beat until combined, about 1 minute. Add egg yolk and beat until incorporated. Reduce speed to low and add in the flour/baking powder and mix for a minute, or until the dough is formed.
Turn dough out on to the counter and shape it into a 9 inch roll to form an even cylinder. Wrap it in parchment paper, roll it again until you feel like it’s a good cylinder shape. Refrigerate for 2 hours.
Heat the oven to 325 degrees. Line two baking sheets with parchment and slice the chilled dough into 1/4 inch rounds and place on baking sheet, and bake for 10-12 minutes.