Preheat oven to 250 degrees F (120 degrees C). Line 4 baking sheets with parchment paper.
Beat egg whites in a glass or metal bowl until foamy and soft peaks form. Gradually add white sugar, continuing to beat until mixture holds stiff peaks, about 5 minutes. Lift your beater or whisk straight up: the egg whites will form sharp peaks.
Mix ground almonds and confectioners' sugar together in a separate bowl; fold into egg white mixture. Transfer mixture to a piping bag; pipe mixture into 2-inch long by 1/2-inch thick mounds onto the prepared baking sheets.
Bake in the preheated oven until cookies are dry and lightly golden brown, about 45 minutes. Transfer cookies to a wire rack to cool completely.
Melt chocolate in the top of a double boiler over simmering water, stirring frequently and scraping down the sides with a rubber spatula to avoid scorching.
Dip each cookie in the melted chocolate using a fork until cookie is completely coated. Shake off excess chocolate. Arrange cookies on the parchment-lined baking sheets; refrigerate until set.