In a large mixing bowl, cream the softened butter and granulated sugar together for about 4 minutes, or until the mixture is light and fluffy. Be sure to scrape down the sides of the bowl. Add in the egg, egg yolk, and vanilla extract, then continue mixing for another minute until fully combined.
Gently fold in the flour, baking powder, and salt until a soft dough forms. Shape the dough into a ball, wrap it tightly in plastic wrap, and refrigerate for 30 minutes to chill.
Preheat your oven to 350°F (175°C). On a lightly floured surface, roll out the chilled dough with a rolling pin to a thickness of about 1/4 to 1/3 inch. Use a round cookie cutter to cut out circles from the dough.
Place the cookie rounds onto a parchment-lined, light-colored baking sheet. Bake for 8 to 9 minutes, then remove from the oven and allow the cookies to cool completely on a wire rack.
Once cooled, spread a generous layer of caramel dip on top of each cookie.
In a microwave-safe bowl, add the milk chocolate and heat on 50% power in 45-second intervals, stirring between each until the chocolate is fully melted and smooth. Use a whisk to make it creamy and glossy.
Spread the melted chocolate evenly over the caramel layer on each cookie. Place the cookies in the refrigerator for about 10 minutes to allow the chocolate to set. Serve the cookies chilled or at room temperature, depending on your preference.