Heat oven to 350ºF. In large bowl, break up cookie dough. Stir in chocolate baking bits. Shape dough into 3/4-inch balls; place 2 inches apart on ungreased cookie sheets. With glass dipped in sugar, flatten each ball slightly.
Bake 8 to 10 minutes or until edges are golden brown. Immediately remove from cookie sheets; place on cooling racks. Cool completely, about 15 minutes.
In medium microwavable bowl, microwave vanilla baking chips on High 20 to 30 seconds or until melted, stirring every 15 seconds. Stir in frosting until smooth. For each sandwich cookie, spread 1 to 2 teaspoons frosting mixture on bottom of 1 cookie. Top with second cookie, bottom side down; press gently.