Heat oven to 350degreesF. 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.
To melt the baking chips in the microwave, place them in small microwavable bowl with the shortening. Microwave uncovered on High 30 to 60 seconds, stirring every 15 seconds, until melted. If the mixture starts to firm up while dipping the cookies, simply microwave 10 to 15 seconds to melt again.