Beat egg whites in a glass, metal, or ceramic bowl until medium peaks form. Sprinkle in white sugar with mixer running; beat until thoroughly combined. Fold in ground almonds and bread crumbs until evenly combined. Let meringue batter rest for 10 to 15 minutes.
Preheat oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Stir confectioners' sugar and cocoa powder together in a small bowl.
Beat 1 cup butter in a large bowl until smooth. Add confectioners' sugar mixture in 2 to 3 additions, mixing thoroughly after each addition. Beat in vanilla extract and salt until combined.
Scoop meringue batter onto baking sheets in 2-tablespoon portions.
Bake in the preheated oven until firm but not browned, 10 to 12 minutes. Cool on the baking sheets for 5 minutes. Transfer cookies to a cooling rack to cool completely, about 10 minutes.
Flip each meringue cookie over; frost with 1 to 2 tablespoons of the butter mixture. Arrange on a flat plate or baking sheet.
Freeze meringue cookies until firm, 30 to 45 minutes.
Combine semisweet chocolate and 6 tablespoons butter in a microwave-safe bowl. Microwave in 30-second intervals, stirring after each interval, until glaze is smooth.
Dip each cookie into the glaze, frosted-side down, until completely coated. Refrigerate or freeze until set.
