In a large bowl with a hand or a stand mixer, cream butter and powdered sugar until smooth.
Add vanilla and salt, then mix until smooth.
Add flour, 1 cup at a time, mixing between each addition until completely mixed.
If dough is too sticky to roll at this point, chill for 20 minutes.
Otherwise, divide dough in half. Roll each half out to 1/4-inch thick between two pieces of wax paper or parchment paper.
Chill at least 2 hours or up to overnight.
Preheat oven to 350°F. Line 3 cookie sheets with parchment paper or silicone baking mats.
Cut circles of dough, re-rolling as needed. I used an approximately 2-inch round cookie cutter. You can also cut them into squares or any size/shape.
These don’t spread, so you don’t need to space them more than an inch or two on the cookie sheets. Bake for about 14-18 minutes (depending on size of cookie and thickness) until they start to get golden around the edges.
Once cooled, turn half of the cookies upside down and fill each with about 1-2 tablespoons of dulce de leche, topping with an additional cookie to form a sandwich. Tip: Place your dulce de leche in a plastic bag or piping bag and pipe onto each cookie to make filling them easier.
Store in an airtight container for up to 3 days or freeze for up to a month.
Serving suggestion: dust with powdered sugar for a pretty look.