Start by making the caramel so it has plenty of time to cool. See notes in the post above. Add the sugar to a small saucepan. Have the remaining ingredients and a jar ready to go. You have to move quickly since caramel is easy to burn.
Turn the heat to medium and melt the sugar, stirring constantly. Once it's melted and has turned a medium amber color, remove from heat and add the butter and heavy cream while stirring. Place the pan back over the heat and stir constantly until the caramel is smooth. Let the caramel boil for 30 seconds then pour into a jar to cool and thicken.
To make the shortbread, cream together the butter, sugar, vanilla and salt. Add the flour and mix until combined. Place the dough in between 2 pieces of parchment paper and roll into a flat disc. Refrigerate for 30 minutes. After 30 minutes, preheat oven to 350℉.
Remove dough from fridge and roll out evenly about ¼" thick. Cut out shapes using a 3-inch cookie cutter, you should get about 12 cookies. Place each cookie onto a cookie sheet lined with parchment paper and bake for about 10 minutes. Edges will be a light golden brown and centers will look matte.
Remove from oven and let them set on the pan for about 5 minutes before removing to a cooling rack to cool completely. Once cooled, spread a small spoonful of the thickened caramel into the centers of each cookie. Leave room around the edges for the caramel to spread.
Melt the chocolate chips and oil over a double boiler or in the microwave. Let cool off a bit before gently spreading the chocolate over the caramel. Let the chocolate set in the freezer for about 5 minutes before enjoying.