For the Shortbread Cookies:
1. In a large bowl using an electric mixer or a wooden spoon, beat butter, icing sugar and salt until combined. Add the flour and stir in. The dough will be stiff, so you may have to use your hands to incorporate all the flour.
2. Turn the dough out onto a piece of plastic wrap, pat into a disk about 1/2 inch thick. Wrap and chill until firm, about 1 hour. Note: You can keep the dough chilled in the fridge for up to 3 days. Remove the dough about an hour before baking.
3. When ready to bake, preheat oven to 350°F (175°C). Line two baking sheets with parchment paper and set aside.
4. Unwrap the dough and place on a lightly floured piece of parchment or waxed paper. With a lightly floured rolling pin, roll dough about 1/8 inch thick (if dough cracks, let it warm up slightly).
5. Cut out cookies using a round cutter, then re-roll scraps and cut out again. If the dough gets too soft, just re-wrap it and chill it for about 15 minutes. Place cookies 1 inch apart on prepared baking sheets and bake until barely beginning to brown, 12 – 15 minutes. Transfer to wire racks to cool completely.
6. Form sandwiches: Place about 1 teaspoon of dulce de leche between two cookies, squeezing them together gently. Roll in shredded coconut if you so desire.
For the Dulce de Leche:
1. Place a non-reactive pot (ceramic or stainless steel, a pot that doesn't conduct heat very well, but once they get hot they stay warm for a long time) over high heat and let it heat up. Once it's hot, sprinkle in a little sugar. Once they start to melt (it will happen quickly), sprinkle in a little more. Continue sprinkling in sugar a bit at a time, letting each addition melt. Start to add more and more at a time, swirling the pan between additions, until the full 1 cup of sugar has been added. If you need to, use a wooden spoon to gently stir the unmelted sugar into the caramel.
2. Once your sugar has melted entirely, lower the heat and immediately add one cup of the milk, being careful as you do so as it will bubble up. Use a wooden spoon to break up the chunks of caramel, stirring it until the caramel melts. Once the mixture begins to thicken, add the second cup of milk and reduce the mixture again. Reserve the final cup of milk.
3. In a small bowl, whisk together the 2 remaining tablespoons of sugar with the cornstarch in a large bowl. Add about 1/4 cup of the remaining cup of milk, whisking to ensure no lumps form. Pour in the remaining milk, whisking to combine. Then pour in the caramel mixture, whisking constantly to temper the mixture.
4. Return the mixture to the pot and cook over low heat, whisking frequently, until the mixture thickens, about 20 - 30 minutes. As it cooks down, monitor it carefully to prevent it from burning. Once cooked, transfer to a bowl and allow it to cool completely before filling your cookies. Store any leftovers in a sealed container in the fridge for up to a week.
