Pre-heat the oven to 300, with the rack placed in the lower third of the oven.
Grease a 9 x 9 inch non-stick baking pan with butter or cooking spray.
MAKE THE SHORTBREAD
In a medium bowl using a hand mixer, beat butter and sugar on medium high speed until light and fluffy, about 3 minutes.
Add the vanilla, reduce speed to low, and carefully add the flour and salt until just combined.
Mix in the butterscotch chips with a wooden spoon until evenly distributed,, scraping down the sides of the bowl as needed.
Press the dough lightly into the prepared pan using a rubber spatula and refrigerate for 20 minutes.
Score the dough with a knife of bench (pastry) scraper into eighths one direction and quarters in the other to make 32 rectangular cookies.
Before placing in the oven, lightly pierce the dough all over the top with a fork.
Bake the bars until firm and slightly golden brown on the edges, about 50-60 minutes (in my oven it was 55 minutes.)
Immediately cut through the scoring with a sharp knife or bench (pastry) scraper to separate the bars. Leave them in the pan to cool completely.
DIP THE COOKIES IN CHOCOLATE
Melt the dark and milk chocolate in a small sauce pan with shallow water and a bowl fitted on top (shallow enough not to let the bowl touch the water) on medium heat. Stir occassionally until melted and combined. You can also melt the chocolate in the microwave, 30 seconds at a time, stirring after each 30 seconds until all the chocolate is melted.
Remove the cookies from the pan and place on a cookie rack lined sheet pan or a parchment paper lined cookie sheet.
Dip half of each cookie in the melted chocolate, scraping any excess lightly with the side of the bowl, and place back on the baking sheet. Allow the cookies to set, about 30 minutes.
Store in an airtight container in the refrigerator for up to 2 weeks.