Heat oven to 375°F. Combine all cookie ingredients except flour and 1 cup mini chocolate chips in large bowl. Beat at medium speed until creamy. Reduce speed to low. Add flour; beat until mixture forms a dough. Stir in 1 cup mini chocolate chips by hand. Shape dough into 1-inch balls.
Place 2 inches apart onto ungreased cookie sheets. Flatten each ball to 1 1/2-inch circle with bottom of glass dipped in flour.
Bake for 5 to 7 minutes or until set. (DO NOT OVER BAKE.) Let stand 2 minutes; remove from cookie sheets. Cool completely on wire rack.
Combine all frosting ingredients in small bowl. Beat at low speed until smooth. (Add additional milk, one teaspoonful at a time, for desired frosting consistency.)
Frost cooled cookies. Place cookies onto waxed paper. Place 1/2 cup mini chocolate chips and shortening in small microwave-safe bowl. Microwave on HIGH, stirring every 30 seconds, until smooth (60 to 90 seconds).
Drizzle thin lines of chocolate over frosting with teaspoon. Let stand until chocolate is set (at least 30 minutes).