In medium bowl, stir cookie mix, butter, egg, lime peel and 1/2 teaspoon of the ginger until soft dough forms.
In small bowl, mix sugar and remaining 1/4 teaspoon ginger. Shape dough into 36 (1-inch) balls.
Roll balls in sugar mixture. On ungreased cookie sheets, place balls 2 inches apart.
Bake 7 to 9 minutes, or until edges begin to brown and center is set. Cool 1 to 2 minutes.
Remove from cookie sheets to cooling rack. Cool completely, about 30 minutes.
Place baking chips and oil in small resealable freezer plastic bag. Microwave on High for 45 to 60 seconds, turning bag over after 25 seconds. Squeeze bag until chips are melted and smooth.
Cut small tip off one corner of bag, and drizzle over cookies.
