COMBINE 2/3 cup granulated sugar, butter, egg yolk, milk and vanilla extract in large mixer bowl. Beat until creamy. Gradually beat in flour, cocoa and salt. Cover; refrigerate for 1 hour.
PREHEAT oven to 350° F.
SHAPE dough into 1-inch balls; roll in 1/2 cup granulated sugar. Place 2 inches apart on ungreased baking sheets. Press thumb into tops to make 1/2-inch-deep depressions.
BAKE for 10 to 12 minutes or until sides are set but centers are still slightly soft. Place 1 Nestlé NestEgg in center of each cookie. Cool cookies on baking sheets for 2 minutes; remove to wire racks to cool completely.
COMBINE powdered sugar, butter, milk and vanilla extract in small mixer bowl; whisk until smooth. Drizzle over cookies.