Remove the labeling from the sweetened condensed milk and place the can on its side in a pot of boiling water. Lower the heat and simmer for 3 hours. Make sure the water covers the top of the can at all times (you will have to pour in more water from time to time). Remove can from water, allow to cool slightly, then open and stir in salt. Set aside.
for the gingerbread shortbread
In a stand mixer, whip butter and brown sugar until combined.
In a separate bowl, combine flour, spices, and salt. Pour into mixer, pulsing until combined.
Separate dough in half and pound into disks. Wrap each disk in plastic wrap and refrigerate for at least 30 minutes (or up to 24 hours).
Preheat oven to 350°F. Line two large baking sheets with parchment paper. Set aside.
Remove one disk of dough from the fridge and place on a well-floured work surface. Use a rolling pin to roll dough out to 1/4 inch thickness.
Using a 3-inch fluted edge cookie cutter, cut out disks of dough and place onto baking sheets. Use a 1-inch fluted edge cutter to cut out the center of half of the disks of dough. You can repeat this process again with your leftover scraps of dough.
Repeat entire process with second disk of dough.
Bake cookies for 8-10 minutes. The cookies should be slightly soft to the touch. Allow to cool for 10 minutes on the baking trays, then transfer to a cooling rack to finish cooling completely.
Dust the center-cut cookies with powdered sugar. Place a rounded teaspoon of dulce de leche in the center of a full cookie and then sandwich it with the powdered-sugar cookie. Repeat with remaining cookies.