How to Make It
Preheat oven to 300°F with oven racks in the top and lower third of oven. Beat together butter and granulated sugar in the bowl of a stand mixer on medium speed until well combined, about 1 minute. Gradually add powdered sugar, and beat until smooth, stopping to scrape down sides of bowl as needed. Stir in salt. Add egg whites, 1 at a time, beating well after each addition. Stir in vanilla extract. Gradually add flour, and beat on low speed until batter is smooth, about 30 seconds.
Transfer batter to a piping bag fitted with a 1/4-inch round tip. Pipe 2- x 1-inch ovals (about 36) on 2 baking sheets lined with parchment paper, leaving 1 1/2-inches between each oval. Bake in preheated oven until edges are golden brown, 14 to 18 minutes, rotating pans after 10 minutes. Let cookies cool on baking sheets for 10 minutes. Transfer cookies to a wire rack to cool completely, about 30 minutes.
Meanwhile, stir together dulce de leche and salt.
Transfer dulce de leche to a piping bag fitted with a 1/4-inch round tip. Pipe about 2 teaspoons mixture onto half of the cookies, leaving a 1/4-inch border. Sandwich with remaining cookies, and press gently to spread filling to edges.