Heat oven to 350°F. In large bowl, beat 1/2 cup butter, 1/2 cup powdered sugar, the salt and 1 teaspoon vanilla with electric mixer on medium speed, scraping bowl occasionally, until blended. Gradually beat in 1 to 1 1/4 cups flour until soft dough forms.
Shape teaspoonfuls of dough into balls. On ungreased cookie sheets, place balls 2 inches apart. With thumb or handle of wooden spoon, make indentation in center of each.
Bake 12 to 15 minutes or until edges are lightly browned. Meanwhile, in small bowl, beat cream cheese, 1 cup powdered sugar, 2 tablespoons flour and 1 teaspoon vanilla on medium speed until well blended. Stir in walnuts and coconut.
Immediately remove cookies from cookie sheets to cooling racks. Spoon about 1/2 teaspoon filling into each cookie. Cool completely, about 30 minutes.
In 1-quart saucepan, heat chocolate chips, 2 tablespoons butter and the water over low heat, stirring occasionally, until chips are melted. Remove from heat. With spoon, beat in 1/2 cup powdered sugar until smooth. Frost cooled cookies. Store covered in refrigerator.