Preheat the oven to 350°F (175°C). Lightly grease a 12-cup muffin tin or line with paper liners.
In a large bowl, cream together 1 cup softened unsalted butter and 1/2 cup granulated sugar until light and fluffy.
Gradually add 2 cups all-purpose flour and 1/4 teaspoon salt to the butter mixture, mixing until a dough forms.
Divide the dough evenly among the 12 muffin cups and press firmly into the bottom and slightly up the sides to form a shortbread base.
Bake the shortbread bases for 18-20 minutes or until lightly golden. Remove from oven and allow to cool completely in the pan.
In a medium saucepan, combine 1 (14-ounce) can sweetened condensed milk, 1/2 cup packed light brown sugar, 4 tablespoons unsalted butter, and 2 tablespoons light corn syrup.
Cook over medium heat, stirring constantly, until the mixture thickens and turns a golden caramel color, about 10 minutes. Remove from heat and stir in 1 teaspoon vanilla extract.
Pour the caramel evenly over the cooled shortbread bases in the muffin tin. Refrigerate for at least 1 hour to set.
In a microwave-safe bowl, combine 8 ounces chopped semisweet chocolate and 1 tablespoon unsalted butter. Microwave in 30-second intervals, stirring after each, until smooth and fully melted.
Pour the melted chocolate over the set caramel layer in the muffin tin, spreading evenly.
Refrigerate the cookie cups for at least 30 minutes or until the chocolate is firm.
Carefully remove the millionaire shortbread cookie cups from the muffin tin and serve.