Heat oven to 350°F. Remove half of cookie dough from wrapper; refrigerate remaining dough until needed.
Sprinkle about 1/4 cup of flour onto work surface; coat sides of half of dough with flour. With rolling pin, roll out dough to 1/4-inch thickness, adding additional flour as needed to prevent sticking.
With floured 3-inch star-shaped cookie cutter, cut out dough stars. Gently brush excess flour from stars; place 2 inches apart on ungreased cookie sheet. Repeat with remaining half of dough.
Bake 7 to 9 minutes or until light golden brown. Cool 1 minute; remove from cookie sheet to cooling racks. Cool completely, about 15 minutes.
In 1-quart saucepan, heat baking chips and 2 tablespoons shortening over low heat about 4 minutes, stirring occasionally, until chips are melted and smooth. Remove from heat. Dip half of each cookie into vanilla coating, allowing excess to drip off. Place cookies on waxed paper-lined cookie sheet; refrigerate until vanilla coating is set, about 30 minutes.