In a large bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add the 1 cup powdered sugar, the granulated sugar, and salt. Beat until combined, scraping sides of bowl occasionally. Add egg, orange peel, and vanilla; beat until combined. Beat in the 1/3 cup finely ground almonds. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour. Divide dough into three portions. Cover and chill about 2 hours or until dough is easy to handle.
Preheat oven to 350°F. Lightly grease a cookie sheet or line with parchment paper; set aside. On a surface dusted with powdered sugar, roll one portion of dough at a time to 1/8 to 1/4 inch thick. Using a fluted round and/or square 2- to 2 1/2-inch cookie cutter, cut out dough, making an equal number of each shape. Place cutouts 1 inch apart on the prepared cookie sheet.
Bake in the preheated oven for 8 to 10 minutes or until tops are very light brown. Carefully transfer to a wire rack; cool completely.
Within two hours of serving, spread 1 rounded teaspoon of dulce de leche on the bottom of a cookie. Spoon about 1 teaspoon melted chocolate over dulce de leche; use the back of a spoon to gently spread chocolate. Top with another cookie, bottom side down. Repeat with remaining cookies. Sift with powdered sugar.
Place filled sandwich cookies in a single layer in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months. To serve, thaw cookies, if frozen.