Beat ½ cup butter, white sugar, egg yolk, 2 tablespoons milk, and 1 teaspoon vanilla extract until light and fluffy. Combine flour, cocoa, and salt; gradually add to butter mixture. Cover and chill for 1 hour until firm enough to roll into balls.

Lightly beat egg white in a small bowl.

Preheat oven to 350°F (180°C).

Shape dough into 1-inch balls, dip balls in egg white, and roll them in chopped nuts. Place cookies on greased baking sheets. Make an indentation with your thumb in the center of each cookie.

Bake cookies for 10-12 minutes or until centers set.

Prepare the filling by mixing confectioners' sugar, 1 tablespoon butter, 2 teaspoons milk, and ¼ teaspoon vanilla extract in a small bowl until smooth.