Place each shortbread cookie in cup of a greased muffin tin. In 2-quart saucepan over medium-low heat, combine butter, sugar and corn syrup. Heat to a full boil, stirring constantly with a wooden spoon. Boil 3 minutes, stirring constantly.
Slowly pour in sweetened condensed milk, stirring constantly. Continue cooking over low heat until candy thermometer reaches 220-228 degrees F. Remove from heat.
Stir in vanilla. Beat until creamy. Immediately stir in toasted coconut and mix well.
Spoon mixture by teaspoonfuls over shortbread cookies. Cool completely. Remove cooled cookies from muffin tin onto waxed paper.
Melt chocolate chips and drizzle thinly in stripes over cookies and let chocolate harden at room temperature.